Question

the sides of a triangle are in ratio 3 is to 5 is to 7 if the perimeter is 75 find area

Answer 1

Answer:

sides are 15, 25, 35 cm you can find the area using herons formula it is

Step-by-step explanation:

square root of s(s-a)(s-b)(s-c)

where s = 1/2 of the perimeter of the triangle

Answer 2

Answer:

Given :-

• The sides of a triangle are in the ratio of 3 : 5 : 7.
• The perimeter of a triangle is 75.

To Find :-

• What is the area of a triangle.

Solution :-

Let,

$\mapsto \bf{First\: Side =\: 3x\: cm}$

$\mapsto \bf{Second\: Side =\: 5x\: cm}$

$\mapsto \bf{Third\: Side =\: 7x\: cm}$

According to the question,

$\implies \sf 3x + 5x + 7x =\: 75$

$\implies \sf 8x + 7x =\: 75$

$\implies \sf 15x =\: 75$

$\implies \sf x =\: \dfrac{\cancel{75}}{\cancel{15}}$

$\implies \sf\bold{\purple{x =\: 5\: cm}}$

Hence, the required sides are :

❒ First Side :

$\leadsto \sf First\: Side =\: 3x\: cm$

$\leadsto \sf First\: Side =\: 3 \times 5\: cm$

$\implies \sf\bold{\green{First\: Side =\: 15\: cm}}$

❒ Second Side :

$\leadsto \sf Second\: Side =\: 5x\: cm$

$\leadsto \sf Second\: Side =\: 5 \times 5\: cm$

$\leadsto \sf\bold{\green{Second\: Side =\: 25\: cm}}$

❒ Third Side :

$\leadsto \sf Third\: Side =\: 7x\: cm$

$\leadsto \sf Third\: Side =\: 7 \times 5$

$\leadsto \sf\bold{\green{Third\: Side =\: 35\: cm}}$

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

$\clubsuit$ Semi-Perimeter Of A Triangle Formula :

$\footnotesize\mapsto \sf\boxed{\bold{\pink{Semi-Perimeter_{(Triangle)} =\: \dfrac{a + b + c}{2}}}}$

Given :

• First Side (a) = 15 cm
• Second Side (b) = 25 cm
• Third Side (c) = 35 cm

According to the question by using the formula we get,

$\implies \sf Semi-Perimeter_{(Triangle)} =\: \dfrac{15 + 25 + 35}{2}$

$\implies \sf Semi-Perimeter_{(Triangle)} =\: \dfrac{75}{2}$

$\implies \sf\bold{\purple{Semi-Perimeter_{(Triangle)} =\: 37.5\: cm}}$

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

$\clubsuit$ Area Formula by using Heron's Formula :

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

where,

• s = Semi-Perimeter of a triangle

According to the question by using the formula we get,

$\small\longrightarrow \sf Area_{(Triangle)} =\: \sqrt{37.5(37.5 - 15)(37.5 - 25)(37.5 - 35)}$

$\small\longrightarrow \sf Area_{(Triangle)} =\: \sqrt{37.5(22.5)(12.5)(2.5)}$

$\small\longrightarrow \sf Area_{(Triangle)} =\: \sqrt{37.5 \times 703.125}$

$\small\longrightarrow \sf Area_{(Triangle)} =\: \sqrt{26367.1875}$

$\small\longrightarrow \sf\bold{\red{Area_{(Triangle)} =\: 162.37(approx)\: cm}}$

${\small{\bold{\underline{\therefore\: The\: area\: of\: triangle\: is\: 162.37\: cm\: .}}}}$