Question

the sides of a triangle are in the ratio 5 ratio 12 ratio 13 and its perimeter is 150 cm. find the area of the triangle

Answer 1

Heya....hope it helps

Answer 2

Hey friend,
Here is the answer you were looking for:

Let the sides of triangle be 5x, 12x and 13x

We know that
perimeter = a + b + c

150 = 5x + 12x + 13x

150 = 30x

$\frac{150}{30} = x \\ \\ 5 = x \\ \\ x = 5 \\ \\ so \\ 5x \\ = 5 \times 5 \\ = 25 \\ \\ 12x \\ = 12 \times 5 \\ = 60 \\ \\ 13x \\ = 13 \times 5 \\ = 65 \\ \\ so \: the \: the \: sides \: of \: triangle \: are \: 25 \: 60 \: and \: 65 \\ \\ semi \: perimeter \: = \frac{a + b + c}{2} \\ \\ s = \frac{25 + 60 + 65}{2} \\ \\ s = \frac{150}{2} \\ \\ s = 75 \\ \\ so \\ area \: of \: triangle \\ ( \: according \: to \: heron \: s \: formula) \\ = \sqrt{s (s - a)(s - b)(s - c)} \\ \\ = \sqrt{75(75 - 25)(75 - 60)(75 - 65)} \\ \\ = \sqrt{75(50)(15)(10)} \\ \\ = \sqrt{75 \times 50 \times 15 \times 10} \\ \\ = \sqrt{562500} \\ \\ = 750 {cm}^{2}$

Hope this helps!!!

@Mahak24

Thanks...
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