Question

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 360 square yards? Round to the nearest tenth of a yard.
17.1 yards
34.2 yards
39.2 yards
152.6 yards

Answer 1

Correct Answer:
Option A. 17.1 Yards

Solution:
Let the height of trapezium is x yards. According to the given data, we can express the lengths of bases in terms of height.

The short base is 3 yards greater than the height, so measure of short base will be (x+3) yards.

The longer base is 5 yards greater than the height, so measure of longer base will be (x+5) yards.

Area of trapezium is given to be 360 square yards.

Area of trapezium = 0.5 x (Height) x (Sum of Bases)

Using the values, we get:

$360=0.5(x)(x+3+x+5) \\ \\ 720=x(2x+8) \\ \\ 2 x^{2} +8x-720=0 \\ \\ 2( x^{2} +4x-360)=0 \\ \\ x^{2} +4x-360=0 \\ \\ x= \frac{-4+- \sqrt{16-4(1)(-360)} }{2} \\ \\ x= \frac{-4+- \sqrt{1456} }{2} \\ \\ x = 17.1 , -21.1$

Since the height cannot have a negative value, we conclude that the height of trapezium rounded to nearest tenth of a yard will be 17.1 yards.