The length of a rectangle is three times its width. If the perimeter is at most 112 centimeters, what is the greatest possible value for the width?

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cestdugateauhcorr · Accepted Answer

Step 1The perimeter of a rectangle is       p    =    2    l    +    2    w   where p is the perimeter, l is the length and w is the width.We are given the length is three times the width or       l    =    3    w  So we can substitute 3w for l in the formula for the perimeter of a rectangle to get:      p    =    2          (      3      w      )        +    2    w        p    =    6    w    +    2    w        p    =    8    w  The problem also states the perimeter is at most 112 centimeters. At most means the perimeter is less than or equal to 112 centimeters. Knowing this inequality and know the perimeter can be expresses as 8w wecan write and solve for w:      8    w    ≤    112   centimeters                    8        w            8        ≤          112      8       centimeters      w    ≤    14   centimeters

The length of a rectangle is three times its width.

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