Problema Solution
A deck for a home is in a shape of a triangle. The length of the base of the triangle is 9 feet longer than its height. If the area of a triangle is 68 square feet, find the length of the base
Answer provided by our tutors
let
h = the height of the triangle
a = the length of the base, a>0
the length of the base of the triangle is 9 feet longer than its height
a = 9 + h
h = a - 9
the area of a triangle is 68 square feet
(1/2)ah = 68
plug h = a - 9 into the last equation
(1/2)a(a - 9) = 68
by solving we find
a = 17 ft
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the base is 17 feet long.