Question

select the correct choice from each dropdown.
rectangle x has length 30 and width 24. rectangle y has length 40 and width 26. rectangle z has length 20 and width 16.
a. is rectangle x a scaled copy of rectangle y? no
b. is rectangle y a scaled copy of rectangle z? no
c. is rectangle x a scaled copy of rectangle z? yes

Explanation:

Step1: Check if Rectangle X is a scaled copy of Rectangle Y

For two rectangles to be scaled copies, the ratios of their corresponding sides must be equal.
For length: $\frac{30}{40}=\frac{3}{4}$
For width: $\frac{24}{26}=\frac{12}{13}$
Since $\frac{3}{4}
eq\frac{12}{13}$, Rectangle X is not a scaled copy of Rectangle Y.

Step2: Check if Rectangle Y is a scaled copy of Rectangle Z

For length: $\frac{40}{20} = 2$
For width: $\frac{26}{16}=\frac{13}{8}$
Since $2
eq\frac{13}{8}$, Rectangle Y is not a scaled copy of Rectangle Z.

Step3: Check if Rectangle X is a scaled copy of Rectangle Z

For length: $\frac{30}{20}=\frac{3}{2}$
For width: $\frac{24}{16}=\frac{3}{2}$
Since the ratios of length and width are equal ($\frac{3}{2}$), Rectangle X is a scaled copy of Rectangle Z.

Answer:

a. No
b. No
c. Yes