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?

Answer 1

#27"cm"#.

Let #l and w# be the length and width of the rectangle, resp..
Then, by what is given, #l=3w.........(1)#.
The perimeter #p# of the rectangle is #p=2(l+w)...........(2)#, and,
using what is given, #p le 72............(3)#
From #(1)-(3)," we have, "2(3w)+2w le 72, i.e., 8w le 72#
#:. w le 9, &, so, l=3w le 27.#

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

#27"cm"#.
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Answer 2

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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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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