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Answer 1 · 2017-03-27T04:31:27

Perimeter of the larger rectangle is $72ft$
Perimeter of the smaller rectangle is $32ft$

There are two possible answers to this question because there is no indication of whether the scaling factor is up or down.

When a dimension is scaled, its resulting size is usually much smaller than full scale so it can be represented by a drawing or scale model.

In this case the exercise may be to measure out a larger or smaller rectangle for use on a field.

We know the perimeter of the original rectangle is $48ft$

We also know that the perimeter $P$ of the rectangle is defined as:

$P=2L+2W$ which states $P$ is directly proportional to $L+W$

And 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 $1.5$
This means the sum of the dimensions $L+W$ is scaled by $1.5$

It also means that the Perimeter is scaled by $1.5$ as it is proportional to $L+W$ .

Then if we upscale (enlarge) the dimension of a $48ft$ field by $1.5$ ,

$P=48*1.5=72ft$

Then if we downscale (reduce) the dimension of a $48ft$ field by $1.5$ ,

$P=48/1.5=32ft$

The answer can be tested by choosing some values for $L,W$

Original: $L=14, W=10; P=48=2(14)=2(10)$

Upscale: $L=14*1.5, W=10*1.5; P=72=2(21)=2(15)$

Downscale: $L=14/1.5, W=10/1.5; P=32=2(9.3)=2(6.7)$