Two similar 2

Two similar polygons have corresponding sides 15 inches and 6 inches. If the area of the first is 2700 square inches, what is the area of the second?

Correct answer:

S₂ =  432 in²

Step-by-step explanation:

$$\begin{gathered} S_1=2700{\text{in}}^2 \\ a=15\text{in} \\ b=6\text{in} \\ r=b:a=6:15=\frac{2}{5}=0.4=2:5 \\ {S}_1=K\cdot a^2 \\ {S}_2=K\cdot b^2 \\ {S}_2=K\cdot (r\cdot a{)}^2 \\ {S}_2=K\cdot r^2\cdot a^2=r^2\cdot (K\cdot a^2) \\ {S}_2=r^2\cdot S_1 \\ {S}_2=r^2\cdot S_1=0.4^2\cdot 2700=432{\text{in}}^2 \end{gathered}$$

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