Question

A local improvement store sells different sized of storage sheds. The most expensive shed has a footprint that is 15 feet wide by 21 feet long, The least expensive has a footprint that is 10 feet wide by 14 feet long. Are the footprints of the two sheds similar? If so, tell whether the footprint of the least expensive shed in a enlargement or a reduction, and find the scale factor from the most expensive shed to the least expensive shed/

Answer 1

Answer:

Question 1: Are the footprints of the two sheds similar?

• Yes, the two sheds are similar.

Question 2: Tell whether the footprint of the least expensive shed is an enlargement or a reduction,

• It is a reduction

Question 3: Find the scale factor from the most expensive shed to the least expensive shed

• The scale factor is 3/2

Explanation:

Question 1: Are the footprints of the two sheds similar?

The footprints of the two sheds will be similar if their measures are proportional.

The ratio of the measures of the footprint of the most expensive shed is:

• width/length = 15 feet / 21 feet = 5 / 7

The ratio of the measures of the footprint of the least expensive shed is:

• width/length = 10 feet / 14 feet = 5 / 7

Since, the two ratios are equal, you conclude that the corresponding dimensions are proportional and the two sheds are similar.

Question 2: Tell whether the footprint of the least expensive shed is an enlargement or a reduction.

A reduction is a similar transformation (the image and the preimage are similar)  that maps the original figure into a smaller one.

Since the dimensions of the foot print of the least expensive shed, 10 feet wide by 14 feet long, are smaller than the dimensions of the most expensive shed, 15 feet wide by 21 feet long the you conclude that the former is a reduction of the latter.

Question 3: Find the scale factor from the most expensive shed to the least expensive shed.

To find the scale factor from the most expensive shed to the least expensive shed, you divide the measures of the corresponding dimensions. You can do it either with the widths or with the lengths.

Using the widths, you get:

• width of the foot print of the most expensive shed / width of the foot print of the least expensive transformation

• 15 feet / 10 feet = 3/2.

That means that the scale factor from the most expensive shed to the least expensive shed is 3/2.

Using the lenghts, you should obtain the same scale factor:

• length of the foot print of the most expensive shed / length of the foot print of the least expensive transformation

• 21 feet / 14 feet = 3/2. Such as expected.