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Question
In the following figure, area of ΔPQR is 20 cm2 and area of ΔPQS is 44 cm2. Find the length RS, if PQ is perpendicular to QS and QR is 5 cm.
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Solution
Given, area of ΔPQR = 20 cm2 and area of ΔPQS = 44 cm2
We know that,
Area of triangle = `1/2` × Base × Height
∴ Area of ΔPQR = `1/2` × PQ × QR ...[∵ PQ ⊥ QR]
⇒ 20 = `1/2` × PQ × 5
⇒ `(20 xx 2)/5` = PQ ...[∵ QR = 5 cm, given]
⇒ PQ = 8 cm
∴ Area of ΔPQS = `1/2` × PQ × QS
⇒ 44 = `1/2` × 8 × QS
⇒ QS = `(44 xx 2)/8` ...[∵ PQ = 8 cm]
⇒ QS = 11 cm
Now, RS = QS – QR = 11 – 5 = 6 cm
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