Question

The size of the triangle are in the ratio 5:15 :30 and its perimeter 150cm. Find area of the triangle.

Answer 1

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correct Question :-

The area of a triangle is 150 cm2 and its sides are in the ratio 3 : 4 : 5. What is its perimeter?

Given:-

sides of triangle = 3:4:5

area of triangle = $150 cm^2$

to find :-

Perimeter of the triangle

assumptions :-

let the sides be 3x, 4x ,5x

therefore perimeter = 12x

semiperimeter = 12 x /2 = 6x

step by step solution :-

• using heron's formulae

area = $\sqrt(s(s-a)(s-b)(s-c)$

• putting values

area = $\sqrt(6x(6x-3x)(6x-4x)(6x-5x)$

area = $\sqrt(6x(3x)(2x)(x)$

150= $6x^2$

$x^2 = \frac{150}{6}$

$x^2 = 25$

$x = 5cm$

• putting value of x in perimeter

perimeter = 12x = 12 * 5 = 60cm

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