The base of a triangle is 4cm longer than its altitude. If the area of the triangle is 48 sq.cm, the find its base and altitude.

Question

Philoid · Accepted Answer

let the base of the triangle be x cm and altitude be y cm

Given base = 4 + y

Area of the triangle = 1/2 × base × altitude

48 = 1/2 × (4 + y) × y

⇒ 96 = 4y + y²

⇒ y² + 4y – 96 = 0

⇒ y² + 12y - 8 y – 96 = 0

⇒ y( y + 12) - 8 ( y + 12) = 0

⇒ (y - 8) ( y + 12) = 0

⇒ y = 8 or - 12

Since altitude cannot be negative ∴ y = 8

⇒ base = 4 + 8 = 12 cm

Hence, Base = 12 cm; Altitude = 8 cm