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:
[tex]\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}[/tex]
which has two solutions but one is negative, i.e., not applicable. The good solution for base is [tex]4+2\sqrt{47}\approx 17.71 ft[/tex].
Since we know the height is 8 ft less than the base, the height must be 9.71ft
