Find the area and perimeter of a trangle
Whose sides are 30cm , 40cm 50cm​

2 thoughts on “Find the area and perimeter of a trangle<br />Whose sides are 30cm , 40cm 50cm​”

1. Question :–

   • Find the area and perimeter of a triangle whose sides are 30 cm, 40 cm and 50 cm.

   Answer :–

   • Perimeter of the triangle = 120 cm.
   • Area of the triangle = 600 cm².

   To find :–

   • The area and perimeter of a triangle whose sides are 30 cm, 40 cm and 50 cm.

   Solution :–

   • Before finding the area of the triangle, let’s find it’s perimeter!

   We know that :–

   • Perimeter of a triangle = Sum of all it’s sides.

   Here,

   • The sides are 30 cm, 40 cm and 50 cm.

   Therefore

   [tex] \hookrightarrow\boxed{\bf Perimeter = 30 + 40 + 50}[/tex]

   [tex] \hookrightarrow \boxed{\bf Perimeter = 120 \: cm.}[/tex]

   –––––––––––––––––––––––––––––––––––––––––

   • Now, before finding the area of the triangle, let’s find it’s semi-perimeter!

   We know that :–

   [tex] \underline{ \boxed{ \sf Semi-perimeter = \dfrac{a + b + c}{2} }}[/tex]

   Where,

   • a = First side.
   • b = Second side.
   • c = Third side.

   Here,

   • First side = 30 cm.
   • Second side = 40 cm.
   • Third side = 50 cm.

   Therefore,

   [tex] \leadsto \bf Semi-perimeter = \dfrac{30 + 40 + 50}{2} [/tex]

   [tex] \leadsto \bf Semi-perimeter = \dfrac{120}{2} [/tex]

   [tex] \leadsto \bf Semi-perimeter = 60 \: cm[/tex]

   —————————————–

   • Now let’s find the area of the triangle using Heron’s formula, as we know it’s semi-perimeter!

   Area of a triangle is :–

   [tex] \sf\sqrt{s \: (s – a) \: (s – b) \: (s – c)} [/tex]

   Where,

   • s = Semi-perimeter.
   • a = First side.
   • b = Second side.
   • c = Third side.

   Here,

   • Semi-perimeter = 60 cm.
   • First side = 30 cm.
   • Second side = 40 cm.
   • Third side = 50 cm.

   Therefore,

   [tex] \hookrightarrow \rm A =\sqrt{60 \: (60 \!-\! 30) \: (60 \!-\! 40) \: (60\! – \!50)} [/tex]

   [tex] \hookrightarrow\rm A =\sqrt{60 \: (30) \: (20) \: (10)} [/tex]

   [tex] \hookrightarrow\rm A =\sqrt{60 \times 30 \times 20 \times 10} [/tex]

   [tex] \hookrightarrow \rm A =\sqrt{360000} [/tex]

   [tex] \hookrightarrow\rm A =600 \: {cm}^{2} [/tex]

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2. Answer:

   120cm

   Step-by-step explanation:

   the perimeter of triangle=sum of three sides

   =30+40+50

   =120

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