Question

the length of sides of a triangle in the ratio 3:4:5 and its perimeter of triangle is 144cm find are of triangle​

Answer 1

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

perimeter = 144 cm

》 3x + 4x + 5x = 144

》 12x = 144

》 x = 12

3x = 3(12) = 36 cm

4x = 4(12) = 48 cm

5x = 5(12) = 60 cm.

let a = 36 cm, b = 48 cm, c = 60 cm.

s = a+b+c / 2= 36+48+60 /2 = 72.

area of triangle =

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

$= \sqrt{72(72 - 36)(72 - 48)(72 - 60)}$

$= \sqrt{72 \times 36 \times 24 \times 12} = \sqrt{746496}$

$= 864 {cm}^{2}$