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

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

anonymous · Answer

Area of a trapezoid= (longer base + shorter base)/2 * height. Let height = h. Shorter base= h+3 Longer base = h+5 Since you want area of 360, 360 = (h+3 + h+5)/2 * h Simplify, 360 = (2h+8)/2 * h 360 = (h+4)*h 360 = h^2 +4h h^2 +4h - 360 = 0 Solving the quadratic eqn, ( http://www.wolframalpha.com/input/?i=x^2+%2B4+x-360) you will get h = 17.1