2017Q11(b)(ii)Similarity (With Applications to Maps and Models)

NumericalEasy1 mark

11(b)

PQR is a triangle. S is a point on the side QR of ΔPQR such that ∠PSR = ∠QPR. Given QP = 8 cm, PR = 6 cm and SR = 3 cm

Figure for this question

Find the length of QR and PS

Topic: Similarity / scale factor

Previous-year question practice database

Answer

Solution diagram

Solution diagram

Exam answer

From ΔPQR ∼ ΔSPR:

PR/SR = PQ/SP = QR/PR.

Given PR=6, SR=3, PQ=8.

PR/SR = 2.

8/SP = 2 SP = 4 cm.

QR/6 = 2 QR = 12 cm.

Answer: QR = 12 cm; PS = 4 cm.

Explanation

Corresponding sides of similar triangles are proportional. The scale factor is 2.

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