Question

(a) If $△ A BC \sim △ PQR$ in which $A B = 6$ cm, $BC = 4$ cm, $A C = 8$ cm and $PR = 6$ cm, then find the length of $(PQ + QR)$ .

(b) In the given figure, $\frac{QR}{QS} = \frac{QT}{PR}$ and $∠1 = ∠2$ , show that $△ PQS \sim △ TQR$ .

Approach

Given $△ A BC \sim △ PQR$ with sides $A B = 6$ cm, $BC = 4$ cm, $A C = 8$ cm, and $PR = 6$ cm. Corresponding sides are proportional: $\frac{A B}{PQ} = \frac{BC}{QR} = \frac{A C}{PR}$ . Solve for $PQ$ and $QR$ and find their sum.

Step-by-step working

1
$\frac{6}{PQ} = \frac{4}{QR} = \frac{8}{6} \Rightarrow \frac{A B}{PQ} = \frac{A C}{PR}$
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2
$PQ = \frac{6 \times 6}{8} = \frac{9}{2} = 4.5$ cm
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3
$QR = \frac{4 \times 6}{8} = 3$ cm
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4
$PQ + QR = 4.5 + 3 = 7.5$ cm
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Concepts used

similar trianglesproportional sidescorresponding sidesprove similarityfind length

Approach

Step-by-step working

Concepts used

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