Question

the height of a triangular truss is 8ft less than the base. the amount of drywall needed to cover the triangular area is 86ft^2. find the base and height of the triangle to the nereast tenth of a foot.

Answer 1

base = 17.71 ft

height = 9.71ft

Explanation:

Since we are not given the base and heigh directly, to answer this question we need two equations: (1) one to express the area (A) of a triangle, and (2) one describing the fact that height (h) and the base (b) lengths are related. Setting up and solving the system of these two equations for base leads to a quadratic equation:

`(1)/(2)b\cdot h =A=86 ft^2\\h = b-8\\\rightarrow\\(1)/(2)b(b-8)=(1)/(2)b^2-4b=86\\(1)/(2)b^2-4b-86=0\implies\\b=4\pm2√(47)`

which has two solutions but one is negative, i.e., not applicable. The good solution for base is
`4+2√(47)\approx 17.71 ft`.

Since we know the height is 8 ft less than the base, the height must be 9.71ft