Question

The difference between the semi perimeter and the sides of a triangle ABC are 8cm 7cm and 5 cm respectively find the area of the triangle​

Answer 1

Answer:

20√14 cm²

Step-by-step explanation:

Given Sides of a triangle are 8 cm, 7 cm and 5 cm.

Let us assume semi-perimeter as 's'.

Difference between semi-perimeter and sides are 8 cm, 7 cm, 5 cm.

(i) s - a = 8 cm

(ii) s - b = 7 cm

(iii) s - c = 5 cm.

On adding (i), (ii),(iii) we get

⇒ s - a + s - b + s - c = 20

⇒ 3s - (a + b + c) = 20 {∴ s = (a + b + c)/2 (or) 2s = a + b + c}

⇒ 3s - (2s) = 20

⇒ s = 20

∴ Area of the triangle = √s(s - a)(s - b)(s - c)

= √20 * 8 * 7 * 5

= √5600

= 20√14 cm²

Therefore, area of the triangle = 20√14 cm².

Hope it helps!