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

Answer:

The rectangle which is similar to the given rectangle is:

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

Step-by-step 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:

$\dfrac{36}{30}=\dfrac{9}{6}\\\\\dfrac{6}{5}=\dfrac{3}{2}$

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:

$\dfrac{36}{44}=\dfrac{9}{11}\\\\\dfrac{9}{11}=\dfrac{9}{11}$

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:

$\dfrac{36}{64}=\dfrac{9}{8}\\\\\dfrac{9}{16}=\dfrac{9}{8}$

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:

$\dfrac{36}{72}=\dfrac{9}{12}\\\\\dfrac{1}{2}=\dfrac{3}{4}$

since, the two ratios are not equal.

Hence, the figure are not similar.