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Here are two rectangles.

6 cm

10 cm

8 cm

12 cm

Jim says,

"The two rectangles are similar because 8 + 4 = 12 and 6+4=10

Is Jim correct?

Explain your answer.

Answer: No Jim is not correct

Step-by-step explanation: The dimensions of the two rectangles have been given as;

Rectangle A, L = 6 and W = 10

Rectangle B, L = 8 and W = 12

In order to determine if both rectangles are similar, both corresponding sides must have a similar ratio. That means the ratio of L:W in rectangle A must be equal to that of rectangle B. Hence in rectangle A, the ratio becomes,

Ratio = 6:10

Ratio = 6/10

Ratio = 3/5

In rectangle B, the ratio also becomes

Ratio = 8:12

Ratio = 8/12

Ratio = 2/3.

Since 3/5 ≠ 2/3, the rectangles cannot be said to be similar.

Yet another way to check for similarity is by using the ratio of each corresponding side to compare the other, that is, the ratio of both lengths compared to the ratio of both widths. In other words ratio of length A to length B must be equal to the ratio of width A to width B.

Simply put, the ratios should be expressed as follows;

Ratio = 6:8 (Length)

Ratio = 6/8

Ratio = 3/4

And the other ratio is;

Ratio = 10:12 (Width)

Ratio = 10/12

Ratio = 5/6

Since 3/4 ≠ 5/6, then it is incorrect to conclude that both rectangles are similar