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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
avatar+89876 
+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

 

 

cool cool cool

CPhill  Mar 28, 2018

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