Question

The difference between the semiperimeter and the sides of a $\Delta ABC$ are 8 cm, 7 cm and 5 cm respectively. Find the area of the triangle.

Answer 1

the difference between semi perimeter (s) and sides of a triangle are 8,7, and 5
which means

(s-a) =8
(s-b) = 7
(s-c) = 5

where a,b,c are the length of the sides of the triangle ABC
Let the semi-perimeter of the triangle be s.
Let the sides of the triangle be a, b and c.
Given:s – a = 8,s – b = 7 ands – c = 5
Adding all the above equations, we get
(s – a) + (s – b) + (s – c) = 8 + 7 + 5
⇒ 3s – (a + b + c) = 20
⇒ 3s – 2s = 20 $(\because \frac{a+b+c}{2})$
⇒ s = 20 cm

Area of the triangle formula

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

=$\sqrt{20\times 8\times 7\times 5}$

= $\sqrt{5600}$

=74.83 $c{m}^2$