WIthoitgle are in the ratio 11:19:24 and its perimeter is 540 cm. Find

1.	WIthoitgle are in the ratio 11:19:24 and its perimeter is 540 cm. Find the area of the triangle.
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 = 540cm11x + 19x + 24x = 540 cm⇒ 54x = 540cm⇒ x = 10 Sides of triangle are11x = 11 × 10 = 110cm19x = 19 × 10 = 190cm24x = 24 × 10 = 240cmSemi 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

WIthoitgle are in the ratio 11:19:24 and its perimeter is 540 cm. Find the area of the triangle.

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 = 540cm11x + 19x + 24x = 540 cm⇒ 54x = 540cm⇒ x = 10

Sides of triangle are11x = 11 × 10 = 110cm19x = 19 × 10 = 190cm24x = 24 × 10 = 240cmSemi 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