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

Answer:

base = 17.71 ft

height = 9.71ft

Step-by-step 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:

$\frac{1}{2}b\cdot h =A=86 ft^2\\h = b-8\\\rightarrow\\\frac{1}{2}b(b-8)=\frac{1}{2}b^2-4b=86\\\frac{1}{2}b^2-4b-86=0\implies\\b=4\pm2\sqrt{47}$

which has two solutions but one is negative, i.e., not applicable. The good solution for base is  $4+2\sqrt{47}\approx 17.71 ft$.

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