Question

The height of a triangle is 4 feet more than four times the length of the base. The area is 24 square feet. Find the base and the height. Show your work and explain the steps you used to find the solution in order to receive full credit.

Answer 1

Use the given information to create equations to help solve the problem.
H= 4+ 4B
A=24 square feet

Know that the area of a triangle formula is 1/2 x b x h.
A=1/2 x b x h

Plug in the known values and solve for the base.
24= .5 x B x (4+4B)
48=B(4+4B)
48=4B+4B^2
12= B + B^2
0=B^2 + B -12
0=(B+4)(B-3)
B= -4, 3

This solution gives us two answers, so plug both into the formula to find the correct answer.
24=.5 x -4 x (4+4(-4))
48= -4 x (-12)
48=48

24= .5 x 3 x (4+4(3))
48= 3 x (4+12)
48= 3(16)
48=48

It looks like both work, so either answer is correct.