Question

The cross-section of a lean-to shelter is in the shape of a triangle. The base of the triangle is

10​ feet more than twice its height. If the area of the triangle is
104​ square feet, determine the length of the base and the height of the triangle in feet.

Answer 1

The dimensions of the triangle is

• height of the triangle = 8 feet

• base of the triangle = 26 feet

how to find the length

We use the area of triangle, given by the formula

= 1/2 base * height

where area = 104, height = x

104 = 1/2 (2x + 10) * x

104 = x² + 5x

x² + 5x - 104

using calculator to solve

x = -13 or 8

We take the positive value x = 8

The height of the triangle = 8 feet

The base of the triangle = 2(8) + 10 = 26 feet