# 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.

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

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