Question 51

In $$\triangle ABC, \angle A = 90^\circ$$, M is the midpoint of $$BC$$ and $$D$$ is a point on $$BC$$ such that $$AD \perp BC$$. If $$AB = 7$$ cm and $$AC = 24$$ cm, then $$AD : AM$$ is equal to:

Solution

By triplet 7-24-25,

BC = 25 cm

M is the midpoint of BC so,

BM = $$\frac{BC}{2}$$

BM = 25/2 = 12.5 cm

By property,

AM = BM = 12.5 cm

$$AD \perp BC$$ so,

BC.AD = AC⋅AB

25$$\times AD = 7 \times 24$$
AD = 168/25 = 6.72

AD : AM = 6.72 : 12.5 = 336 : 625

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