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

mathelp
Mar 28, 2018

#1**+1 **

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

CPhill
Mar 28, 2018