Question : The area of two similar triangles TUV and PQR are $18 \ \text{cm}^2$ and $32 \ \text{cm}^2$, respectively. If $TU=6\ \text{cm}$, then PQ is equal to:
Option 1: 4 cm
Option 2: 8 cm
Option 3: 2 cm
Option 4: 64 cm
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Correct Answer: 8 cm
Solution :
If TUV and PQR are similar triangles, then
$\frac{\text{Area of triangle TUV}}{\text{Area of triangle PQR}}=\frac{TU^2}{PQ^2}$
⇒ $\frac{18}{32}=\frac{6^2}{PQ^2}$
⇒ $PQ^2=\frac{36\times 32}{18}$
⇒ $PQ^2=64$
⇒ $PQ=\sqrt{64}=8$ cm
Hence, the correct answer is 8 cm.
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