In ΔABC, ∠A = 90o, M is the midpoint of BC and D is a point on BC such that AD ⊥ BC. If AB = 7 cm and AC = 24 cm, then AD : AM is equal to:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e 336 : 625.
| Understanding/Application |
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By triplet 7-24-25
BC = 25 cm M is the mid-point of BC so, BM = BC/2 = 25/2 = 12.5 cm By property, AM = BM = 12.5 cm |
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AD ⊥ BC So, Triangles ADC and BAC are similar: So, BC/AC = AB/AD ⇒ BC × AD = AC × AB ⇒ 25 × AD = 7 × 24 ⇒ AD = 168/25 = 6.72 Hence, AD : AM = 6.72 : 12.5 = 336 : 625 |
