Question

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Answer 1

PQRS is a parallelogram. So the angles on one side are supplementary, i. e., their sum is 180°.

QR is extended to N. If ∠PSR is let as x°, ∠QRS will be 180 - x° (Angles on one side are supplementary).

∠QRS and ∠NRS are linear pairs. ∴ ∠NRS will be 180 - ∠QRS = 180 - (180 - x)° = 180 - 180 + x° = x°

∴∠PSR = ∠NRS = x°. Also ∠PSR and ∠NRS are alternate angles.

Consider ΔPMS and ΔNRS.

∠PSR = ∠NRS (Alternate angles)

∠PMS = ∠RNS (Right angles = 90°)

Two angles are equal. ∴ ΔPMS ~ ΔNRS.

As both triangles are similar, sides opposite to equal angles are in the same ratio.

$\frac{PS}{SR} = \frac{PM}{SN} \\ \\ = \frac{PS}{8.2} = \frac{4.8}{6} = \frac{48}{60} = \frac{4}{5} \\ \\ \\ PS = \frac{4}{5} \times 8.2 = \frac{32.8}{5} = \frac{328}{50} = \bold{6.56\ cm}$

∴ PS = 6.56 cm

Thank you. Have a nice day.

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