NumericalEasy1 mark
6(iii)
In the given diagram ∆ADB and ∆ACB are two right angled triangles with ∠ADB = ∠BCA = 90°. If AB = 10 cm, AD = 6 cm, BC = 2.4 cm and DP = 4.5 cm
Find area ∆APD : area ∆BPC
Topic: Similarity / scale factor
Previous-year question practice database
Answer
Exam answer
We know that, Ratio of area of similar triangles is equal to the square of the corresponding sides. ∴ Area of △APD / Area of △BPC = AD² / BC² = 6² / (2.4)² = (6 × 6) / (2.4 × 2.4) = (1 × 1) / (0.4 × 0.4) = (10 × 10) / (4 × 4) = 100 / 16 = 25 / 4 = 25 : 4. Hence, area △APD : area △BPC = 25 : 4.
Explanation
Use similarity to equate the relevant corresponding-side ratios; for area questions, square the corresponding-side ratio.
More from Similarity (With Applications to Maps and Models)
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