Question

The base of a triangle is seven more than twice the height. The area of the triangle is 135 square meters. Find the measures of the base and height of the triangle.

Answer 1

Height = 10 m

Base = 27 m

Explanation:

The base of a triangle is seven more than twice the height

The area of the triangle is 135 m²

Height = x

Base = 2x + 7

Area of a triangle =
`(1)/(2)` × base × height

∴

`(1)/(2)` × (x) × (2x + 7) = 135

2x² + 7x - 270 = 0

Applying the quadratic formula we get;

x = 10 or -13.5

Since we can't have a length being negative, the height of this triangle is 10 m

The base = 2(10) + 7 = 27