Question

Given a rectangle with a length of 36 and a width of 9, which rectangle is similar? A) rectangle with a length of 30 and a width of 6 B) rectangle with a length of 44 and a width of 11 C) rectangle with a length of 64 and a width of 8 D) rectangle with a length of 72 and a width of 12

Answer 1

we can use the ratio between the given sides to find the similar rectangle

given 36/9= 4
A-- 30/6=5
B-- 44/11= 4
C-- 64/8= 8
D--72/12=6

As you can see the ratio of B matches with our given rectangle

Answer 2

The rectangle which is similar to the given rectangle is:

B) rectangle with a length of 44 and a width of 11.

Explanation:

Two figures are said to be similar if the ratio of each of the corresponding sides of the two figures are equal.

Given a rectangle with a length of 36 and a width of 9.

A)

rectangle with a length of 30 and a width of 6.

The ratio of the corresponding sides is given by:

`(36)/(30)=(9)/(6)\\\\(6)/(5)=(3)/(2)`

since, the two ratios are not equal.

Hence, the figure are not similar.

B)

rectangle with a length of 44 and a width of 11.

The ratio of the corresponding sides is given by:

`(36)/(44)=(9)/(11)\\\\(9)/(11)=(9)/(11)`

since, the two ratios are equal.

Hence, the figure are similar.

C)

rectangle with a length of 64 and a width of 8.

The ratio of the corresponding sides is given by:

`(36)/(64)=(9)/(8)\\\\(9)/(16)=(9)/(8)`

since, the two ratios are not equal.

Hence, the figure are not similar.

D)

rectangle with a length of 72 and a width of 12.

The ratio of the corresponding sides is given by:

`(36)/(72)=(9)/(12)\\\\(1)/(2)=(3)/(4)`

since, the two ratios are not equal.

Hence, the figure are not similar.