Question

Consider that the length of rectangle A is 21 cm and its width is 7 cm. Which rectangle is similar to rectangle A?

Answer 1

Question is incomplete, complete question is given below.

Consider that the length of rectangle A is 21 cm and its width is 7 cm. Which rectangle is similar to rectangle A? A) A rectangle with a length of 9 cm and a width of 3 cm. B) A rectangle with a length of 20 cm and a width of 10 cm. C) A rectangle with a length of 18 cm and a width of 9 cm. D) A rectangle with a length of 27 cm and a width of 3 cm.

Answer:

A) A rectangle with a length of 9 cm and a width of 3 cm.

Explanation:

Given,

Length = 21 cm Width = 7 cm

`Ratio = (Length)/(Width)\\\\Ratio = (21)/(7)=3:1`

For the similarity of rectangle the ratio of length to width of any two rectangles should be equal.

So we have four options given;

A) A rectangle with a length of 9 cm and a width of 3 cm.

`Ratio =(9)/(3)=3:1`

Here the ratio is equal as of rectangle A. So this rectangle is similar to rectangle A.

B) A rectangle with a length of 20 cm and a width of 10 cm.

`Ratio =(20)/(10)=2:1`

Here the ratio is not equal as of rectangle A. So this rectangle is not similar to rectangle A.

C) A rectangle with a length of 18 cm and a width of 9 cm.

`Ratio =(18)/(9)=2:1`

Here the ratio is not equal as of rectangle A. So this rectangle is not similar to rectangle A.

D) A rectangle with a length of 27 cm and a width of 3 cm.

`Ratio =(27)/(3)=9:1`

Here the ratio is not equal as of rectangle A. So this rectangle is not similar to rectangle A.

Thus the correct option is A) A rectangle with a length of 9 cm and a width of 3 cm.