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Question
Area of a triangle PQR right-angled at Q is 60 cm2 (see figure). If the smallest side is 8 cm long, find the length of the other two sides.
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Solution
Given, area of ΔPQR = 60 cm2 and side PQ = 8 cm
∴ Area of ΔPQR = `1/2` × PQ × QR ...[∵ Area of triangle = Base × Height]
⇒ 60 = `1/2` × 8 × QR
⇒ QR = `(60 xx 2)/8`
⇒ QR = 15 cm
In right-angled ΔPQR,
PR2 + PQ2 + QR2 ...[By Pythagoras theorem]
⇒ PR2 + 82 + 152 = 64 + 225
⇒ PR2 = 289
⇒ PR = `sqrt(289)` = 17 cm
Hence, the length of two sides are 15 cm and 17 cm.
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