Question

A rectangle has a perimeter of 48 ft. The length and width are scaled by a factor 1.5. What is the perimeter of the resulting rectangle?

Answer 1

`color(blue)(72 " ft")`

Explanation:

If the dimensions of the rectangle are increased by a scale factor of `3/2` the perimeter will also be increased by a scale factor of `3/2`.

So we have:

`3/2xx48=72 " ft"`

This is because the perimeter is a linear measurement.

Consider a rectangle of length `bba` and width `bb(b)`.

Perimeter is:

`2a+2b` this is linear.

Increasing by a scale factor `f`

length of rectangle `fa` width `fb`

Perimeter:

`2fa+2fb=f(2a+2b)`