Question

rectangle a has length 12 and width 8. rectangle b has length 15 and width 10. rectangle c has length 30 and width 15.

1. is rectangle a a scaled copy of rectangle b? if so, what is the scale factor?
2. is rectangle b a scaled copy of rectangle a? if so, what is the scale factor?
3. explain how you know that rectangle c is not a scaled copy of rectangle b.
4. is rectangle a a scaled copy of rectangle c? if so, what is the scale factor?

Explanation:

Answer:

1.

• Answer: Yes, the scale factor is $\frac{4}{5}$.
• Explanation:
• Step1: Calculate length - scale ratio
• $\frac{12}{15}=\frac{4}{5}$
• Step2: Calculate width - scale ratio
• $\frac{8}{10}=\frac{4}{5}$
• Since the ratios of the corresponding sides are equal, Rectangle A is a scaled - copy of Rectangle B with a scale factor of $\frac{4}{5}$.

2.

• Answer: Yes, the scale factor is $\frac{5}{4}$.
• Explanation:
• Step1: Calculate length - scale ratio
• $\frac{15}{12}=\frac{5}{4}$
• Step2: Calculate width - scale ratio
• $\frac{10}{8}=\frac{5}{4}$
• Since the ratios of the corresponding sides are equal, Rectangle B is a scaled - copy of Rectangle A with a scale factor of $\frac{5}{4}$.

3.

• Answer: The ratio of the lengths is $\frac{30}{15} = 2$, and the ratio of the widths is $\frac{15}{10}=\frac{3}{2}$. Since $\frac{3}{2}

eq2$, the ratios of the corresponding sides are not equal, so Rectangle C is not a scaled copy of Rectangle B.
4.

• Answer: No.
• Explanation:
• Step1: Calculate length - scale ratio
• $\frac{12}{30}=\frac{2}{5}$
• Step2: Calculate width - scale ratio
• $\frac{8}{15}

eq\frac{2}{5}$

• Since the ratios of the corresponding sides are not equal, Rectangle A is not a scaled copy of Rectangle C.