SOLUTION: One base of a trapezoid is 8 cm longer than the other. The height of the trapezoid is 2 cm longer than the shortest base. If the area is 48 cm^2, what are the height and bases?

Algebra ->  Surface-area -> SOLUTION: One base of a trapezoid is 8 cm longer than the other. The height of the trapezoid is 2 cm longer than the shortest base. If the area is 48 cm^2, what are the height and bases?      Log On


   

Question 1154782: One base of a trapezoid is 8 cm longer than the other. The height of the trapezoid is 2 cm longer than the shortest base. If the area is 48 cm^2, what are the height and bases?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
One base of a trapezoid is 8 cm longer than the other.
The height of the trapezoid is 2 cm longer than the shortest base.
If the area is 48 cm^2, what are the height and bases?
:
The area of a trapezoid: A = h%2F2(a+b)
a = the shorter base
b = (a+8), the other base
h = (a+2), the height
:
%28a%2B2%29%2F2(a+(a+8)) = 48
multiply both sides by 2
(a+2)(2a+8) = 96
FOIL
2a^2 + 8a + 4a + 16 = 96
2a^2 + 12a + 16 - 96 = 0
2a^2 + 12a - 80 = 0
divide both sides by 2, solve
a^2 + 6a - 40 = 0
Factors TO
(a+10)(a-4) = 0
positive solution
a = 4 cm is the shorter base
then
4+8 = 12 cm is the longer base
and
4+2 = 6 cm is the height
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Confirm on a calc
6%2F2(4+12) = 48.00