Question

The sides of traingle are in ration 11:19:24 and it's perimeter is 540cm find the area of traingle

Answer 1

Answer:

Ratio of the sides of the triangle = 11 : 19 : 24

Let the common ratio be x then sides are 11x, 19x and 24x

Perimeter of the triangle = 540cm

11x + 19x + 24x = 540 cm

⇒ 54x = 540cm

⇒ x = 10

Sides of triangle are

11x = 11 × 10 = 110cm

19x = 19 × 10 = 190cm

24x = 24 × 10 = 240cm

Semi perimeter of triangle(s)

= 540/2 = 270cm

Using heron's formula,

Area of the triangle

= √s (s-a) (s-b) (s-c)

= √270(270 - 110) (270 - 190) (270 - 240)cm2

= √270 × 160 × 80 × 30

= 7200√2 cm2