The difference between the semi-perimeterand the sides of a ∆ABC are

1.	The difference between the semi-perimeterand the sides of a ∆ABC are 8 cm, 7 cmand 5 cm respectively. The area of thetriangle is(A) 20√7 cm2 B) 10√ 14 cm^2(c) 20√14 cm2 (D) 140 cm2
Answer» 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⇒ s = 20 cm Thus the semi-perimeter is 20 cm a = √s(s-a)(s-b)(s-c) = √2087*5 = √5600 Area = 74.83 cm²

The difference between the semi-perimeterand the sides of a ∆ABC are 8 cm, 7 cmand 5 cm respectively. The area of thetriangle is(A) 20√7 cm2 B) 10√ 14 cm^2(c) 20√14 cm2 (D) 140 cm2

Answer»

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⇒ s = 20 cm

Thus the semi-perimeter is 20 cm

a = √s(s-a)(s-b)(s-c)

= √20*8*7*5

= √5600

Area = 74.83 cm²