Question

The length of base of a triangle is 2cm more than its altitude. The area of triangle is 24cm². Find the altitude and base of the triangle.​

Answer 1

Answer:

Altitude = 8 cm

Base = 6 cm

Step-by-step explanation:

Let the altitude of Δ = x cm

Base = ( x + 2 ) cm

∵ Area of Δ = 1/2  × Base × Altitude

⇒ 24 cm² = 1/2 (x) (x + 2)

⇒ x² + 2x -24 = 0

⇒ x + (6 - 4)x - 48 = 0

⇒ x + 8x - 6x - 48 = 0

⇒ x ( x + 8 ) - 6 ( x + 8) = 0

⇒ (x - 6) (x + 8) = 0

x = 6 , -8

∵ Length cannot be negative.

∴ Base = x = 6 cm

∴ Altitude= x + 2 =  6 + 2 = 8cm