Question

A rectangle has a a perimeter of 72 ft. The length and width are scaled by a factor 3.5.

What is the perimeter of the resulting rectangle?



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Answer 1

We know the perimeter of the original rectangle is 72ft.
We also know that the perimeter P of the rectangle is defined as:
P=2L+2W.
So P is directly proportional to L+W. This means that if L or W were to get bigger, P will get bigger, and if L or W were to get smaller P will get smaller.

The question also states that both L and W are scaled by the same factor of 3.5 .
This means the sum of the dimensions L+W is scaled by 3.5
It also means that the perimeter is upscaled by 3.5 as it is proportional to L+W.
P = 72 ft × 3.5 = 252 ft.

252 ft is the answer.

Answer 2

Formula for perimeter of rectangle:
P=2(L+w)
P=2L+2w
Here Perimeter, p= 72 ft
And scale factor of length and width=3.5 which means rectangle is enlarged.
So perimeter of rectangle= 3.5 x 72
P=252ft

Answer: 252 ft