# The length of a rectangle is 3 times as great as its width. If the perimeter of the rectangle is no more than 72 cm, what is the greatest possible length of the rectangle?

This means that the the greatest possible length of the rectangle is

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Let's denote the width of the rectangle as ( w ) cm. Then, according to the problem, the length of the rectangle would be ( 3w ) cm.

The formula for the perimeter of a rectangle is ( P = 2l + 2w ), where ( P ) is the perimeter, ( l ) is the length, and ( w ) is the width.

Given that the perimeter is no more than 72 cm, we can write:

[ 2(3w) + 2w \leq 72 ]

Simplify and solve for ( w ):

[ 6w + 2w \leq 72 ]

[ 8w \leq 72 ]

[ w \leq \frac{72}{8} ]

[ w \leq 9 ]

So, the width of the rectangle must be no more than 9 cm.

Since the length of the rectangle is three times the width, the maximum length would be ( 3 \times 9 = 27 ) cm.

Therefore, the greatest possible length of the rectangle is 27 cm.

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