Rectangle area change

The sides of the rectangle are 6.6 cm and 4.2 cm. We change its dimensions in a ratio of 5:2. How many times does the rectangle's area change compared to the original rectangle?

Final Answer:

k =  6.25

Step-by-step explanation:

$$\begin{gathered} r=5:2=2.5 \\ {k}_1=r^2=2.5^2=\frac{25}{4}=6\frac{1}{4}=6.25 \\ a=6.6\text{cm} \\ b=4.2\text{cm} \\ x=r\cdot a=2.5\cdot 6.6=\frac{33}{2}=16\frac{1}{2}=16.5\text{cm} \\ y=r\cdot b=2.5\cdot 4.2=\frac{21}{2}=10\frac{1}{2}=10.5\text{cm} \\ {S}_1=a\cdot b=6.6\cdot 4.2=\frac{693}{25}=27\frac{18}{25}=27.72{\text{cm}}^2 \\ {S}_2=x\cdot y=16.5\cdot 10.5=\frac{693}{4}=173\frac{1}{4}=173.25{\text{cm}}^2 \\ k=S_2:S_1=173.25:27.72=\frac{25}{4}=6\frac{1}{4}=6.25=25:4 \\ k=k_1 \end{gathered}$$

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