Question 92

In ΔPQR, S and T are points on side PQ and PR respectively. ST is parallel to QR. If lengths of PS, SQ and PR are 6 cm, 9 cm and 12.5 cm respectively, what is the length of TR?

Solution

ST is parallel to QR and PS = 6 cm and SQ = 9 cm

PR = 12.5 cm

Let TR = $$x$$ cm

=> $$\frac{PS}{SQ} = \frac{PT}{TR}$$

=> $$\frac{6}{9} = \frac{(12.5-x)}{x}$$

=> $$\frac{(12.5-x)}{x} = \frac{2}{3}$$

=> $$37.5-3x=2x$$

=> $$3x+2x=5x=37.5$$

=> $$x=\frac{37.5}{5}=7.5$$ cm

=> Ans - (A)

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