Enlarged rectangle

The rectangle has dimensions of 8 cm and 12 cm. We enlarge it in a ratio of 5:4. What are the circumference and the area of the enlarged rectangle?

Correct answer:

o =  50 cm
S =  150 cm²

Step-by-step explanation:

$$\begin{gathered} a=8\text{cm} \\ b=12\text{cm} \\ {o}_1=2\cdot (a+b)=2\cdot (8+12)=40\text{cm} \\ k=\frac{5}{4}=1.25 \\ o=k\cdot o_1=\frac{5}{4}\cdot 40=\frac{5\cdot 40}{4}=\frac{200}{4}=50\text{cm} \end{gathered}$$

$$\begin{gathered} S_1=a\cdot b=8\cdot 12=96{\text{cm}}^2 \\ S=k^2\cdot S_1={\frac{5}{4}}^2\cdot 96=150{\text{cm}}^2 \end{gathered}$$

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