Question

Find the area of triangle whose sides are in ratio 5:12:13.Its perimeter is 60 cm.

Answer 1

Please let me know whether it is right

Answer 2

Given : sides of triangle are in ratio 5:12:13
Perimeter = 60 cm

Let, $\bf{a}$, $\bf{b}$,$\bf{c}$ be the sides of triangle

$\bf{a}$ = 5x

$\bf{b}$= 12x

$\bf{c}$ = 13x

$\underline{Perimeter \: \: of\: \: triangle = sum \: \:of\: \: all\: \: sides}$

60 = 5x + 12x + 13x

60 = 30x

60/30 = x

2 = x

Value of x = 2

Now,

a = 5x = 5*2 = 10 cm
b = 12x = 12*2 = 24 cm
c = 13x = 13*2 = 26 cm

$\bf{\underline{Semi \: \:perimeter(s)}}$ = $\frac{a+b+c}{2}$

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

= $\frac{60}{2}$

= 30

$\bf{\underline{Area\: \: of \: \:the\: \: triangle :}}$


$\sqrt{s(s - a)(s - b)(s - c)} \\ \\ \sqrt{30(30 - 10)(30 - 24)(30 - 26)} \\ \\ \sqrt{30 \times 20 \times 6 \times 4} \\ \\ \sqrt{2 \times 3 \times 5 \times 2 \times 2 \times 5 \times 2 \times 3 \times 2 \times 2} \\ \\ 2 \times 3 \times 5 \times 2\times 2 \\ \\ = 120 {cm}^{2}$