Answer:
- length: 15.6 yd
- width: 11.6 yd
Explanation:
You want the length and width of a garden with an area of 180 yd² that is 4 yd longer than wide.
Dimensions
Let w represent the width. Then the area is ...
w(w +4) = 180
w² +4w +4 = 184 . . . . . add 4
w +2 = ±√184
w = -2 + 2√46 ≈ 11.6 . . . . . . . . only the positive dimension is useful
The width of the garden is about 11.6 yards; the length is 15.6 yards.
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Additional comment
It can be useful to consider the average (x) of the length and width. Then the area is (x -2)(x +2) = 180, so x² -4 = 180, or x² = 184. This tells us the dimenions are (√184 -2) and (√184 +2).
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