Question

Find the perimeter and area of length 52cm , 56cm,and 60cm​

Answer 1

Answer:

Given :-

• The length of sides of a triangle is 52 cm, 56 cm and 60 cm.

To Find :-

• What is the perimeter and area of triangle.

Solution :-

Given :

• First Side (a) = 52 cm
• Second Side (b) = 56 cm
• Third Side (c) = 60 cm

First, we have to find the perimeter of triangle :

As we know that :

$\footnotesize\bigstar\: \: \sf\boxed{\bold{\pink{Perimeter_{(Triangle)} =\: Sum\: of\: all\: sides\: of\: triangle}}}$

Then the perimeter of triangle is :

$\implies \sf Perimeter_{(Triangle)} =\: a + b + c$

$\implies \sf Perimeter_{(Triangle)} =\: 52 + 56 + 60$

$\implies \sf\bold{\red{Perimeter_{(Triangle)} =\: 168\: cm}}$

${\small{\bold{\underline{\therefore\: The\: perimeter\: of\: triangle\: is\: 168\: cm\: .}}}}$

Now, we have to find the semi-perimeter of a triangle :

As we know that :

$\footnotesize\mapsto \sf\boxed{\bold{\pink{Semi-Perimeter_{(Triangle)} =\: \dfrac{Sum\: of\: all\: side\: of\: triangle}{2}}}}$

Then, the semi-perimeter of a triangle is :

$\implies \sf Semi-Perimeter_{(Triangle)} =\: \dfrac{52 + 56 + 60}{2}$

$\implies \sf Semi-Perimeter_{(Triangle)} =\: \dfrac{\cancel{168}}{\cancel{2}}$

$\implies \sf Semi-Perimeter_{(Triangle)} =\: \dfrac{84}{1}$

$\implies \sf\bold{\purple{Semi-Perimeter_{(Triangle)} =\: 84\: cm}}$

Now, we have to find the area of triangle by using Heron's Formula :

As we know that :

$\footnotesize\mapsto \sf\boxed{\bold{\pink{Area_{(Triangle)} =\: \sqrt{s(s - a)(s - b)(s - c)}}}}$

Given :

• Semi-Perimeter = 84 cm
• First Side = 52 cm
• Second Side = 56 cm
• Third Side = 60 cm

According to the question by using the formula we get,

$\longrightarrow \sf Area_{(Triangle)} =\: \sqrt{84(84 - 52)(84 - 56)(84 - 60)}$

$\longrightarrow \sf Area_{(Triangle)} =\: \sqrt{84(32)(28)(24)}$

$\longrightarrow \sf Area_{(Triangle)} =\: \sqrt{84 \times 32 \times 28 \times 24}$

$\longrightarrow \sf Area_{(Triangle)} =\: \sqrt{1806336}$

$\longrightarrow \sf Area_{(Triangle)} =\: \sqrt{1344 \times 1344}$

$\longrightarrow \sf\bold{\red{Area_{(Triangle)} =\: 1344\: cm^2}}$

${\small{\bold{\underline{\therefore\: The\: area\: of\: triangle\: is\: 1344\: cm^2\: .}}}}$