WAEC Mathematics 2021 Theory — Question 13

Question 13 of 22 from the West African Examinations Council (WAEC) Mathematics 2021 Theory paper, with the correct answer and a full explanation.

8(a). In ΔPQR, ∠PQR=90°. If the area is 216 cm² and |PQ|:|PR| is 3:4, find |PR|.

Model answer

Let |PR|=x, so |PQ|=(3/4)x. By Pythagoras, |QR|=√(x²−(3x/4)²)=(√7/4)x. Area=½×PQ×QR: 216=½×(3x/4)×(√7x/4)=3√7x²/32. x²=216×32/(3√7)=6912/(3√7). Solving, |PR| ≈ 29.5 cm.

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