Question

Is there a proportional relationship between the corresponding sides of each pair

of rectangles?
2
3
A
5
7.5
B
6
8
L
4
6
M

Answer 1

Rectangles A & B: Proportional

Rectangles L & M: Not proportional

Explanation:

A proportional relationship between the corresponding sides of a pair of rectangles means that the ratios of the lengths of corresponding sides of the two rectangles are equal.

`\hrulefill`

Rectangles A and B

In rectangle A, the length is 3 units and the width is 2 units.

In rectangle B, the length is 7.5 units and the width is 5 units.

To determine if there is a proportional relationship between the corresponding sides of the two rectangles, we compare the ratios of their lengths and widths.

• Ratio of lengths: A : B = 3 : 7.5
• Ratio of widths: A : B = 2 : 5

Set the ratios equal to each other:

`\sf (3)/(7.5) = (2)/(5)`

By cross-multiplying, we see that:

5 · 3 = 7.5 · 2

15 = 15

This demonstrates that there is a proportional relationship between the corresponding sides of rectangles A and B.

`\hrulefill`

Rectangles L and M

In rectangle L, the length is 8 units and the width is 6 units.

In rectangle M, the length is 6 units and the width is 4 units.

To determine if there is a proportional relationship between the corresponding sides of the two rectangles, we compare the ratios of their lengths and widths.

• Ratio of lengths: L : M = 8 : 6
• Ratio of widths: L : M = 6 : 4

Set the ratios equal to each other:

`\sf (8)/(6)=(6)/(4)`

By cross-multiplying, we see that:

4 · 8 = 6 · 6

32 = 36

Since 32 ≠ 36, it is evident that there is no proportional relationship between the corresponding sides of rectangles L and M.