SOLUTION: 8. The area of a triangle is 13.5 square meters. Find the base and height of the rectangle if its height is 6 meters greater than its base. Use an equation and the formula ® area o

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 8. The area of a triangle is 13.5 square meters. Find the base and height of the rectangle if its height is 6 meters greater than its base. Use an equation and the formula ® area o      Log On


   

Question 173320: 8. The area of a triangle is 13.5 square meters. Find the base and height of the rectangle if its height is 6 meters greater than its base. Use an equation and the formula ® area of a triangle = 0.5(base)(height).
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Let the base be x, then the height is x%2B6

Since the area is given by A=bh%2F2, you can just substitute:

13.5=%28x%28x%2B6%29%29%2F2

Distribute, collect like terms, and put the equation into standard form for a quadratic:

27=x%5E2%2B6x

x%5E2%2B6x-27=0

Solve this by factoring, recognizing that -3%2A9=-27 and -3%2B9=6.

One of your roots will be a negative value. Exclude that root because it is extraneous introduced by the act of squaring the variable. The other root will be the length of the base.