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 the length of BD and PB
Topic: Similarity / scale factor
Previous-year question practice database
Answer
Exam answer
In △ADB, By pythagoras theorem, => AB² = AD² + BD² => 10² = 6² + BD² => BD² = 100 - 36 => BD² = 64 => BD = √64 = 8 cm. => PB = BD - PD = 8 - 4.5 = 3.5 cm Hence, BD = 8 cm and PB = 3.5 cm.
Explanation
Use similarity to equate the relevant corresponding-side ratios; for area questions, square the corresponding-side ratio.
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