Question

sides of the triangle are in the ratio of 7:24:25 and it's perimeter is 112 find its area​

Answer 1

Answer:

area of triangle = 1/2*base*height

=1/2*24*7

=82

Answer 2

Answer:

let, sides be- 7x , 24x & 25x

A.T.Q

7x + 24x + 25x = 112

56x = 112

x = 112/56

x = 2

therefore, sides are a - 7x = 7*2 = 14

b - 24x = 24*2 = 48

c - 25x = 25*2 = 50

Now,

by herons formula

semi-perimeter (s) = 112/2 = 56

therefore, area of ∆ =

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

$= \sqrt{56(56 - 14)(56 - 48)(56 - 50)}$

$= \sqrt{56 \times 42 \times 8 \times 6}$

$= \sqrt{8 \times 7 \times 7 \times 6 \times 8 \times 6}$

$= \: 8 \times 7 \times 6$

$= \: 336 \: unit {}^{2}$