Question

thr side of a triangle in ratio 5ratio12ratio13 and its perimeter is 150m.find the area of triangle​

Answer 1

ratio of sides of the triangle- 5:12:13.

let the sides be 5x, 12x,13x

perimeter = 150 m

》 5x + 12x + 13x = 150

》30x = 150

》 x = 5

5x = 5(5) = 25 m

12x = 12 ( 5) = 60m

13x = 13(5) = 65 m.

therefore, the sides of the triangle are 25m, 60m,65m.

Here; 25,60,65 are pythogras triplets.

( 25 square + 60 square = 65 square )

》 the triangle with sides 25m, 60m, 65 m forms a right angled triangle.

base = 60m ; height = 25m.

area of triangle = 1/2 × base × height = 1/2 × 60 × 25 = 750 sq.m.

( or )

let a = 25m ; b = 60m ; c = 65cm

s = a+b+c /2. = 25+60+65 /2 = 150/2 = 75.

Now substitute these values in heron's formula to find area of the triangle.

Heron's formula =

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

after solving using this formula u get the same answer 750 sq.m.