Question

1. Find the area of a triangle whose sides are in the ratio 5:12:13 and its perimeter is 60
cm.​

Answer 1

Given -

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Sides of traingle in ratio

5:12:13

Perimeter => 60cm

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Concept -

Find the Area of traingle.?????

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Formula used

$\sqrt{s(s - a)(s - b)(s - c)}$

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Solution.-

Let ,

$a = > 5x \\ \\ b = > 12x \\ \\ c = > 13x \\ \\ perimeter = > 60cm$

$5x + 12x + 13x = 60 \\ \\ 30x = > 60 \\ \\ x = > \frac{60}{30} cm \\ \\ x = > 2cm$

$\color{red}{put \: the \: value \: of \: x \: } \\ \\ 5 \times 2 = 10cm \\ \\ 12 \times 2 = 24cm \\ \\ 13 \times 2 = > 26cm \\ \\ \color{blue} \boxed{s = \frac{a + b + c}{2} } \\ \\ s = > \frac{10 + 24 + 26}{2} \\ \\ s = > \frac{60}{2} \\ \\ \color{hotpink} \boxed{s = > 30cm}$

By Heron s formula.....

$\sqrt{s(s - a)(s - b)(s - c)} \\ \\ \sqrt{30(30 - 10)(30 - 24)(30 - 26)} \\ \\ \sqrt{30(20)(6)(4)} \\ \\ \sqrt{30 \times 20 \times 6 \times 4 } \\ \\ \sqrt{5 \times 6\times 5 \times 4 \times 6 \times 1 \times 4} \\ \\ = > > 5 \times 6 \times 4 \\ \\ = > > 120c {m}^{2}$

Area of Traingle = 120cm²

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Hope it's helps you ☺️✨

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Thanks☺️

Answer 2

$\underline{\huge{\underline{\bold{\purple{Question}}}}}$

Find the area of a triangle whose sides are in the ratio 5:12:13 and its perimeter is 60

cm.

$\underline{\huge{\underline{\bold{\purple{Answer}}}}}$

Given :-

• $\bold{a\;=\;5x}$
• $\bold{b\;=\;12x}$
• $\bold{c\;=\;13x}$
• $\bold{Perimeter\;=60cm}$

To find :-

The area of a triangle.

Steps of Solution

First we have to find all the sides.

• Formula to find all the sides = a + b + c = perimeter.

$\bold{5\;x\;+\;12\;x\;+\;13\;x\;=\;60}$

$\bold{17\;x\;+\;13\;x\;=\;60}$

$\bold{30\;x\;=\;60}$

$x \: = \: \frac{60}{30} \\ x \: = \: 2cm$

$\bold{Therefore\;=\;a=\;5\;x\;=\;5\;x\;2\;=\;10cm}$

$\bold{ \ b=\;12\;x\;=\;12\;x\;2\;=\;24cm}$

$\bold{ \ c\;=\;13\;x\;=\;12\;x\;2\;=\;26cm}$

$\bold s = {\frac{a+b+c}{2}}$

$\bold s = {\frac{10+24+26}{2}}$

$\bold s = {\frac{34+26}{2}}$

$\bold s = {\frac{60}{2}}$

$\bold s = {30}$

• By Herons Formula

$\bold{=\sqrt{s(s - a)(s - b)(s - c)}}\\ \\ = \sqrt{30(30 - 10)(30 - 24)(30 - 26)} \\ \\= \sqrt{30(20)(6)(4)} \\ \\= \sqrt{30 \times 20 \times 6 \times 4 } \\ \\= \sqrt{5 \times 6\times 5 \times 4 \times 6 \times 1 \times 4} \\ \\ = 5 \times 6 \times 4 \\ \\ = 120c {m}^{2}$