+156 A landscaper is designing a flower garden in the shape of a trapezoid. She wants the length of the shorter base to be 3 yards greater than the height, and the length of the longer base to be 5 yards greater than the height. For what height will the garden have an area of 375 square yards? Round to the nearest tenth of a yard.
a. 155.7 yards
c. 39.9 yards
b. 17.5 yards
d. 34.9 yards
+129933 Area of a trapezoid =
height * ( sum of base lengths) / 2
So...let the height = h
One base = h + 3
And the other is h + 5
So...we have this
375 = h [ (h + 3 + h + 5 ] / 2 multiply both sides by 2
750 = h [ 2h + 8 ]
750 = 2h^2 + 8h rearrange as
2h^2 + 8h - 750 = 0
Using the quadratic formula....we get the answer ≈ 17.468 = 17.5 yards (rounded)
"b" is correct
