A lot for sale is shaped like a trapezoid. the bases of the trapezoid represent the widths of the front and back yards. the width of the back yard is twice the width of the front yard. the distance from the front yard to the back yard, or the height of the trapezoid, is equal to the width of the back yard. find the width of the front and back yards, given that the area is 7,500 square feet. round to the nearest foot.

Question

Mathematics

Ali Stanton

4 September, 22:39

A lot for sale is shaped like a trapezoid. the bases of the trapezoid represent the widths of the front and back yards. the width of the back yard is twice the width of the front yard. the distance from the front yard to the back yard, or the height of the trapezoid, is equal to the width of the back yard. find the width of the front and back yards, given that the area is 7,500 square feet. round to the nearest foot.

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Teresa Stewart · Answer 1

Area of a trapezoid = (h/2) (a + b) where h = distance between back and front yards, a = front width and b = back width.

So b = 2a so a = b/2 and h = b so

area = (b/2) (b + b/2) = 7,500

b^2/2 + b^2/4 = 7500

2b^2 + b^2 = 30,000

b^2 = 30,000 / 3 = 10,000

b = 100

so width of the back yard = 100 ft and width of the front is 50 ft