Question

The side of a triangle are in the ratio 5:12:13 ,and its perimeter is 150m find the area of the triangle

Answer 1

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Answer 2

Given that sides of triangle are in ratio

5:12:13

so let the sides be --

5x,12x and 13x

Given Perimeter = 150 m

As we know that Perimeter of triangle = Sum of the sides of triangle

Therefore,

5x + 12x + 13x = 150

30x = 150

x = 150 ÷ 30

x = 5

Therefore, sides of Triangle =

5x = 5(5) = 25m

12x = 12(5) = 60m

13(5) = 65m

Now, When the sides of the triangle are given or has been found then the area of triangle can be calculated by Heron's formula

which is -

$\sqrt{s(s - a)(s - b)(s - c)}$
Where, s is the Semiperimeter and a,b and c are the sides of triangle.

Now,
let a = 25m

b = 60m

c = 65m
________________________________

Semiperimeter (s) = Perimeter ÷ 2

s = 150 ÷ 2

s = 75m

$area \: = \\ \\ \sqrt{s(s - a)(s - b)(s - c)} \\ \\ \sqrt{75(75 - 25)(75 - 60)(75 - 65)} \\ \\ \sqrt{75 \times 50 \times 15 \times 10} \\ \\ \sqrt{562500} \\ \\ = 750 \: m {}^{2}$