{"id":6830,"date":"2021-12-27T08:07:15","date_gmt":"2021-12-27T08:07:15","guid":{"rendered":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/?page_id=6830"},"modified":"2022-01-03T07:47:03","modified_gmt":"2022-01-03T07:47:03","slug":"perimeter-of-a-triangle-formula-solved-examples","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/perimeter-of-a-triangle-formula-solved-examples\/","title":{"rendered":"Perimeter of a Triangle – Formula – Solved Examples"},"content":{"rendered":"

[et_pb_section fb_built=”1″ admin_label=”Section” module_class=”mainsec” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#e0f2fd” z_index=”1″ custom_padding=”5px||5px||true|false” locked=”off” collapsed=”off” global_colors_info=”{}”][et_pb_row column_structure=”3_5,2_5″ custom_padding_last_edited=”on|phone” _builder_version=”4.10.8″ _module_preset=”default” background_color=”#FFFFFF” width=”100%” max_width=”1310px” custom_padding=”|51px|40px|51px|false|true” custom_padding_tablet=”” custom_padding_phone=”|40px|30px|40px|false|true” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}”][et_pb_column type=”3_5″ admin_label=”Column L” _builder_version=”4.9.10″ _module_preset=”default” global_colors_info=”{}”][et_pb_text admin_label=”Acute Angles
\n” _builder_version=”4.11.3″ _module_preset=”default” header_font=”|700|||||||” header_text_align=”left” header_font_size=”50px” header_line_height=”1.18em” custom_padding=”|0px||4px|false|false” header_font_size_tablet=”” header_font_size_phone=”35px” header_font_size_last_edited=”on|phone” global_colors_info=”{}”]<\/p>\n

Perimeter of a Triangle – Formula – Solved Examples<\/h1>\n

[\/et_pb_text][et_pb_text admin_label=”Text” _builder_version=”4.13.1″ _module_preset=”default” text_font_size=”16px” header_2_font=”|600|||||||” header_2_text_color=”#a01414″ header_3_font=”|600|||||||” custom_padding=”15px|15px|54px|4px|false|false” global_colors_info=”{}”]<\/p>\n

Perimeter of a triangle<\/b><\/h2>\n

The perimeter of a triangle is equal to the total sum of the measure of all three sides of that triangle.\u00a0<\/span><\/p>\n

The formula for perimeter is different in different types of triangles based on their properties. We are going to derive the perimeter formula for the following triangles.<\/span><\/span><\/p>\n

    \n
  1. Equilateral Triangle<\/span><\/li>\n
  2. Isosceles Triangle<\/span><\/li>\n
  3. Scalene Triangle<\/span><\/li>\n
  4. Right-angled Triangle<\/span><\/li>\n
  5. Isosceles right-angled Triangle<\/span><\/li>\n<\/ol>\n

    <\/span><\/p>\n

    Perimeter of an equilateral triangle<\/b><\/h2>\n

    In an equilateral triangle, the measure of all sides is equal to each other.<\/span><\/p>\n

    \"\"<\/span><\/p>\n

    In \u25b3PQR<\/span><\/p>\n

    PQ = QR = RP = s = measure of each side<\/span><\/p>\n

    Perimeter = PQ + QR + RP<\/span><\/p>\n

    \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= s + s + s<\/span><\/p>\n

    \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 3s<\/span><\/p>\n

    Hence the perimeter of an equilateral triangle is equal to 3s where \u201cs\u201d is the length of each side.<\/span><\/p>\n

    <\/span><\/p>\n

    Perimeter of an isosceles triangle<\/b><\/h2>\n

    In an isosceles triangle, the measure of the two sides is equal to each other.<\/span><\/p>\n

    \"\"<\/span><\/p>\n

    In \u25b3PQR<\/span><\/p>\n

    PQ = RP = s\u00a0<\/span><\/p>\n

    QR = a<\/span><\/p>\n

    Perimeter = PQ + QR + RP<\/span><\/p>\n

    \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= s + s + a<\/span><\/p>\n

    \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 2s + a<\/span><\/p>\n

    Hence perimeter of an isosceles triangle is equal to (2s + a) where \u201cs\u201d is the measure of one of the two equal sides and \u201ca\u201d is the measure of the third side.<\/span><\/p>\n

     <\/p>\n

    Perimeter of a scalene triangle<\/b><\/h2>\n

    In a scalene triangle, the measure of all sides is unequal.<\/span><\/p>\n

    \"\"<\/span><\/p>\n

    In \u25b3PQR<\/span><\/p>\n

    PQ = r<\/span><\/p>\n

    QR = p<\/span><\/p>\n

    RP = q<\/span><\/p>\n

    Perimeter = PQ + QR + RP<\/span><\/p>\n

    \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= r + p + q<\/span><\/p>\n

    \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= p + q + r<\/span><\/p>\n

    Hence the perimeter of a scalene triangle is equal to (p + q + r), where \u201cp\u201d, \u201cq\u201d, and \u201cr\u201d are the measure of the three sides. <\/span><\/p>\n

     <\/p>\n

    Perimeter of a right-angle triangle<\/b><\/h2>\n

    <\/b><\/p>\n

    \"\"<\/b><\/p>\n

    \u00a0In \u25b3PQR<\/span><\/p>\n

    \u2220PQR = 90\u00b0<\/span><\/p>\n

    PQ = r = leg<\/span><\/p>\n

    QR = p = leg<\/span><\/p>\n

    RP = hypotenuse = h<\/span><\/span><\/p>\n

    h=\\sqrt{p^{2}+r^{2}}<\/span> (pythagoras theorem)<\/span><\/p>\n

    Perimeter = PQ + QR + RP<\/span><\/p>\n

    \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= r + p + h<\/span><\/p>\n

    \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= r+p+\\sqrt{p^{2}+r^{2}}<\/span><\/p>\n

    Hence the perimeter of a right-angle triangle is equal to \\left(r+p+\\sqrt{p^{2}+r^{2}}\\right)<\/span> <\/span>where \u201cp\u201d and \u201cq\u201d are the measure of the legs of the right-angle triangle.<\/span><\/p>\n

     <\/p>\n

    Perimeter of an isosceles right triangle<\/b><\/h2>\n

    In an isosceles right triangle, the two sides other than hypotenuse are equal to each other<\/span><\/p>\n

    \"\"<\/span><\/p>\n

    In \u25b3PQR<\/span><\/p>\n

    \u2220PQR = 90\u00b0<\/span><\/p>\n

    PQ = s = leg<\/span><\/p>\n

    QR = s = leg<\/span><\/p>\n

    RP = hypotenuse = h<\/span><\/p>\n

    h=\\sqrt{s^{2}+s^{2}}<\/span><\/span><\/p>\n

    Perimeter = PQ + QR + RP<\/span><\/p>\n

    \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= s + s + h<\/span><\/p>\n

    \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= s+s+\\sqrt{s^{2}+s^{2}}<\/span><\/span><\/p>\n

    \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 2 \\mathrm{~s}+\\sqrt{2} \\mathrm{~s}<\/span><\/span><\/p>\n

    \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= s(2+\\sqrt{2})<\/span><\/span><\/p>\n

    Hence the area of an isosceles right-angle triangle is equal to \\left[s(2+\\sqrt{2})\\right]<\/span><\/span>, where s is the measure of equal legs.<\/span><\/p>\n

    <\/span><\/p>\n

    Solved Examples<\/b><\/h2>\n

    1. In a right-angled triangle, two sides are equal, having a length of 7 cm. Find the perimeter of this triangle?<\/b><\/b><\/p>\n

    Solution:<\/strong><\/p>\n

    Since two sides of the right-angled triangle are equal, it is an isosceles right triangle\u00a0<\/span><\/p>\n

    Length of the leg = s = 7 cm<\/span><\/p>\n\\text { Perimeter }=s(2+\\sqrt{2})=7(2+\\sqrt{2})=(14+7 \\sqrt{2}) \\mathrm{cm}<\/span>\n

    Hence the perimeter of the triangle is equal to (14+7 \\sqrt{2}) \\mathrm{cm}<\/span>.<\/span><\/p>\n

    <\/span><\/p>\n

    2. The perimeter of \u25b3PQR is equal to 27 inches. Find the measure of each side of the triangle if it is an equilateral triangle?<\/strong>
    <\/span><\/p>\n

    Solution:<\/strong><\/p>\n

    Since it is an equilateral triangle, the length of all the sides are equal to each other<\/span><\/p>\n

    \u00a0s = length of each side<\/span><\/p>\n

    Perimeter\u00a0 = 3s<\/span><\/p>\n

    \u21d2 3s = 27 inches<\/span><\/p>\n

    \u21d2 s = 27\/3 inches = 9 inches<\/span><\/p>\n

    Hence the length of each side is equal to 9 inches.<\/span><\/p>\n

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    Explore Other Topics<\/h1>\n

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    \n
    Geometry<\/a><\/div>\n
    Trigonometry<\/a><\/div>\n
    Operations<\/a><\/div>\n
    Numbers<\/a><\/div>\n<\/div>\n

    [\/et_pb_text][et_pb_text admin_label=”Related Concepts
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    Related Concepts<\/h1>\n

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    \n
    Mensuration Formula<\/a><\/div>\n
    Area of an Isosceles Right Triangle<\/a><\/div>\n
    Area of Equilateral Triangle<\/a><\/a><\/div>\n<\/div>\n

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    Frequently Asked Questions\u00a0<\/span><\/span><\/h1>\n
      <\/ol>\n

      Q1. What is the measure of the angles other than the right-angled in an isosceles right triangle?
      <\/strong><\/h3>\n

      Ans: <\/strong>The two angles in an isosceles right triangle other than the hypotenuse are equal and the measure of each of these angles is 45\u00b0.
      <\/span><\/span><\/p>\n

      Q2. What do you mean by the perimeter of a triangle?
      <\/strong><\/h3>\n

      Ans: <\/strong>The perimeter of a triangle is equal to the total sum of the measure of all three sides of that triangle.<\/strong><\/strong>\u00a0<\/p>\n

      Q3. How much does each angle of a triangle measure, if it is an equilateral triangle?
      <\/strong><\/h3>\n

      Ans: <\/strong>Each angle of a triangle measures 60\u00b0 if it is an equilateral triangle.<\/span><\/span><\/p>\n

      Q4. What is the perimeter of an equilateral triangle?
      <\/strong><\/h3>\n

      Ans: <\/strong>The perimeter of the equilateral triangle ABC is 3a, where a is the length of each side.<\/strong><\/p>\n

      [\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"

      Meta Description: We can calculate the sum of the terms in a geometric progression using the formula S = a(1-r^n)\/(1-r) when r < 1 and S = a(r^n-1)\/(r-1)when r>1<\/p>\n","protected":false},"author":10,"featured_media":0,"parent":714,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"yoast_head":"\nPerimeter of a Triangle - Formula - Solved Examples - mydomain<\/title>\n<meta name=\"description\" content=\"Meta Description: We can calculate the sum of the terms in a geometric progression using the formula S = a(1-r^n)\/(1-r) when r < 1 and S = a(r^n-1)\/(r-1)when r>1\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/perimeter-of-a-triangle-formula-solved-examples\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Perimeter of a Triangle - 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