Question

Question #fdcf3

Answer 1

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

Explanation:

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)`