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2 votes
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

User Yuck
by
7.6k points

1 Answer

2 votes

Answer:

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

User Daprezjer
by
6.5k points
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