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.
Step-by-step explanation:
Given,
Length = 21 cm Width = 7 cm
[tex]Ratio = \frac{Length}{Width}\\\\Ratio = \frac{21}{7}=3:1[/tex]
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.
[tex]Ratio =\frac{9}{3}=3:1[/tex]
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.
[tex]Ratio =\frac{20}{10}=2:1[/tex]
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.
[tex]Ratio =\frac{18}{9}=2:1[/tex]
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.
[tex]Ratio =\frac{27}{3}=9:1[/tex]
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.
