Problema Solution
The front of an A-frame cabin in a national park is in the shape of a triangle, with an area of 14 ft^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
a = the length of the base, a>0
h = the length of the height, h>0
A = 14 ft^2
the formula for area of triangle is A = (1/2)(a*h)
(1/2)(a*h) = 14 multiply both sides by 2
a*h = 28
the height is 1 ft less than twice the base
h = 2a - 1
plug h = 2a - 1 into a*h = 28
a(2a - 1) = 28
by solving we find
a = 4 ft
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h = 2*4 - 1
h = 7 ft
the base of the cabin is 4 ft.
the height of the cabin is 7 ft.