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These figures are similar. The area ofone is given. Find the area of the other.Area = 100 in.28 in.10 in.[? ] in.2

These figures are similar. The area ofone is given. Find the area of the other.Area-example-1
User Maxim Shoustin
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1 Answer

19 votes
19 votes

If the dilation coefficient between two figures is equal to k, the ratio between their areas is k^2.

In our case, the dilation coefficient is


(10)/(8)=(5)/(4)

Then,


\begin{gathered} A_{\text{larger}}=k^2A_(smaller) \\ \Rightarrow A_{\text{smaller}}=\frac{A_{\text{larger}}}{k^2}=(100)/(((5)/(4))^2)=(100)/((25)/(16))=16\cdot4=64 \\ \Rightarrow A_{\text{smaller}}=64 \end{gathered}

Thus, the answer is 64in^2

User Cambria
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