The base of a triangle is 4 cm greater than the height. the area is 48 cm squared. find the height and base of the triangle.

Given information

Area of the triangle = 48 cm²
The base is 4 cm greater than the height


Define height and base

Let height be x
height = x
base = x + 4


Formula: Area of Triangle

Area of triangle = 1/2 x base x height


Substitute x and solve

1/2(x+4)(x) = 48
1/2 (x² + 4x) = 48
x² + 4x = 48 x 2
x² + 4x - 96 = 0
(x - 8)(x + 12) = 0
 x = 8 or x = 12 (rejected, length cannot be negative)


Find base and height

Height = x = 8cm
base = x + 4 = 8 + 4 = 12cm


The height is 8cm and the base is 12 cm