Question

The length of a rectangular parking lot is 50 yards. If the perimeter is less than 180

yards, write and solve an inequality that describes the width of the lot in terms of (w).

Answer 1

w < 40

Explanation:

The formula for the perimeter of a rectangle can be used to write an expression for the perimeter in terms of (w). Then the constraint on the perimeter can be used to write the inequality.

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perimeter

The perimeter of a rectangle is given by the formula ...

P = 2(L +W) . . . . . where L and W represent the length and width

Substituting the given values, we have ...

P = 2(50 +w) = 100 +2w

inequality

The perimeter is less than 180 yards, so we have ...

P < 180

100 +2w < 180 . . . . inequality in terms of w

solution

2w < 80 . . . . . subtract 100

w < 40 . . . . . . divide by 2

The width of the lot is less than 40 yards.