Problema Solution
The front of an A-frame cabin in a national park is in the shape of a triangle, with an area of 33ft^2. If the height is 1 ft less than twice the base, find the base and the height of the front of the cabin.
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Let
x = the base of the triangle, x>0
h = the height of the triangle, h>0
A = 33 ft^2 is the area of the triangle
The height is 1 ft less than twice the base:
h = 2x - 1
The area of the triangle is:
A = (1/2)xh
Plug the values for A and h = 2x - 1 into the last equation:
(1/2)x*(2x - 1) = 33
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x = 6 ft
h = 2*6 - 1
h = 11 ft
The base is 6 feet.
The height is 11 feet.