Question

Find the area of triangle two sides of which are 20 cm and 12 cm and the perimeter is 48 cm.

Answer 1

Answer

(a) Side = 20 cm

(b) Base = 12 cm

(P) Perimeter = 48 cm

Using formulas:

A = √s(s﹣a) (s﹣b) (s﹣c)

P = a + b + c

s = a + b + c / 2

Solving for A:

=> A = 1 / 4 √ - P^4 + 4P^3a + 4P^3b﹣4(Pa)^2﹣12P^2 ab﹣4(Pb)^2 + 8Pa^2b+8Pab^2

=> 1/4 × √﹣48^4 + 4 × 48^ 320+4 × 48^3 × 12﹣4 × (48 × 20)^2﹣12 × 48^2 * 20 × 12﹣4 × (48 × 12)^2 + 8 × 48 × 20^2 × 12 + 8 × 48 × 20 × 12^2

=> 96cm²

Answer 2

Answer: 96 cm^2

Step-by-step explanation:

perimeter = a + b + c

48 = 20 + 12 + c

c = 48 - 32

c = 16

s = 48/2 = 24

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

= √(24 × 4 × 8 × 12)

= 4 × 6 √(2×2×2×2)

= 4×6×2×2

= 96 cm^2