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Given AB = 7 cm, PQ = x cm, PR = 5 cm, AC = 10 cm, BC = y cm, QR = 4.5 cm. If ∆ ABC ~ ∆PQR, find x and y

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4, 6

4, 3

3, 6

3.5, 9

answer is A.

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Detailed Solution

If ∆ ABC ~ ∆PQR, then

$\frac{A B}{P Q} = \frac{B C}{Q R} = \frac{A C}{P R}$

$\frac{7}{x} = \frac{y}{4.5} = \frac{10}{5}$

$\Rightarrow \frac{7}{x} = 2 a n d \frac{y}{4.5} = 2$

$∴ x = 3.5 a n d y = 9$

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