Question

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

triangle is 6 feet more than twice its height. If the area of the triangle is 88 square feet,determine the length of the base and the height of the triangle in feet

Answer 1

Explanation:

Givens

Let the height = x

Let the base = 2*x +6

Let the area = 88 square feet.

Formula

A = Base * height / 2

Solution

88 = (2x + 6)*x/2 Multiply both sides by 2

88*2 = (2x+6)*2*x/2 Combine

176 = (2x + 6)*x Remove the brackets

176 = 2x^2 + 6x Subtract 176 from both sides

0 = 2x^2 + 6x - 176 This factors without the quadratic

0 = (2) (x^2 + 3x - 88)

0 = 2 (x +11)(x - 8)

Note: x + 11 has no meaning. Measurements of this type cannot be minus. What is - 11 feet.

x - 8 =0

x = 8

Answer

height = 8 feet

base = 2*8 + 6

base = 22