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A rectangular garden covers 180 yd^2. The length is 4 yd longer than the width. Find the length and width. Round your answers to the nearest tenth of a yard

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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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A rectangular garden covers 180 yd^2. The length is 4 yd longer than the width. Find-example-1
User Andreas DM
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