Question

Sides of a trianlge are in the ratio11:19:24 and it's perimeter is 540cm. Find the area of the triangle.

Answer 1

$\huge\mathcal\pink{ANSWER}$

Let the sides be 11x, 19x and 24x

11x + 19x + 24x = Perimeter

54x = 540 cm

$x = \frac{540}{54} \: cm$

$x = 10 \: cm$

The sides are :

11x = 110

19x = 190

24x = 240

Area of Δ by heron's formula :

$s = \frac{a + b + c}{2}$

$s = \frac{540}{2}$

s = 270 cm

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

$area = \sqrt{270(270 - 110)(270 -190)(270 - 240)}$

$area = \sqrt{270 \times160 \times80 \times 30 }$

$area = 7200 \sqrt{2} \: {cm}^{2}$

$\huge\mathcal\pink{THANKS}$