Question : The perimeters of two similar triangles XYZ and PQR are respectively 62 cm and 42 cm. If PQ = 21 cm, find XY.
Option 1: 27 cm
Option 2: 28 cm
Option 3: 29 cm
Option 4: 31 cm
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Correct Answer: 31 cm
Solution :
Since the ratio of the corresponding sides of similar triangles is the same as the ratio of their perimeters.
$\therefore \triangle$ XYZ ~ $\triangle$ PQR
$⇒\frac{\text{XY}}{\text{PQ}} = \frac{\text{YZ}}{\text{QR}} = \frac{\text{XZ}}{\text{PR}} = \frac{62}{42}$
$⇒\frac{\text{XY}}{\text{PQ}} = \frac{62}{42}$
$⇒\frac{\text{XY}}{21} = \frac{62}{42}$
$⇒\text{XY} = \frac{62 \times 21}{42}$
$⇒\text{XY} = 31$ cm
Hence, the correct answer is 31 cm.
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