Question

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

Answer 1

Consider a, b and c as the sides of a triangle and s as the semi perimeter

So we get

s - a = 8cm

s - b = 7cm

s - c = 5cm

We know that(s - a) + (s - b) + (s - c) = 8 + 7 + 5

On further calculation

3s - (a + b + c) = 20

We know that a + b + c = 2s

3s - 2s = 20

So we gets = 20

By substituting the value of s

a = s - 8 = 20 - 8 = 12cm

b = s - 7 = 20 - 7 = 13cm

c = s - 5 = 20 - 5 = 15cm

We know that

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

By substituting the values

Area=$$ \sqrt{20(20-12(20-13)(20-15)}$$

So we get

Area=$$ \sqrt{20\times8\times7\times5}$$

It can be written as

Area=$$\sqrt{4\times5\times4\times2\times7\times5}$$

By multiplication

Area=$$ 20\sqrt{14}$$

Therefore, the area of the triangle is $$20\sqrt{14}cm^2$$