- The length of the base of the triangle is 28 feet and
- The height of the triangle is 10 feet.
How to determine the length and height of the triangle?
Given that the cross-section of the lean-to shelter is in the shape of a triangle, its area is the area of a triangle, A = 1/2bh where
- b = length of base and
- h = height
Now, since the base of the triangle is 8 feet more than twice its height, we have that b = 2h + 8
So, A = 1/2bh
= 1/2(2h + 8)h
= h² + 4h
Since the area of the triangle A = 140 ft², we have that
h² + 4h = 140
h² + 4h - 140 = 0
Factorizing, we have
h² + 4h - 140 = 0
h² + 14h - 10h - 140 = 0
h(h + 14) - 10(h + 14) = 0
(h + 14)(h - 10) = 0
h + 14 = 0 or h - 10 = 0
h = -14 or h = 10
Since h cannot be negative, h = 10 ft
Since the length of the base b = 2h + 8
Substititng h = 10 into the equation, we have
b = 2h + 8
b = 2(10) + 8
b = 20 + 8
b = 28 ft
So,
- The length of the base of the triangle is 28 feet and
- The height of the triangle is 10 feet.
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