Question

4) The length and width of a rectangular box

are 10 in. and 8 in., respectively. Another
rectangular box has a length of 15 in. and a
width of 12 in. respectively. Are the length
and width dimensions of the two rectangular
boxes similar?

Answer 1

Explanation:

Yes, the length and width dimensions of the two rectangular boxes are similar.

Two objects are considered similar if they have the same shape, but not necessarily the same size. The ratio of the corresponding sides of two similar objects is called the scale factor.

For the first rectangular box, the ratio of length to width is 10/8, which can be simplified to 5/4.

For the second rectangular box, the ratio of length to width is 15/12, which can be simplified to 5/4 as well.

Since the ratio of the corresponding sides of the two boxes is the same, namely 5/4, we can conclude that the length and width dimensions of the two rectangular boxes are similar.