Question

In a ∆ABC, <A = 90°, AB = 5 cm and AC = 12 cm. If AD is perpendicular to BC, then find AD.

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Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Given:

In ΔABC, angle A = 90º, AD is perpendicular to BC.

AC = 12 cm, AB = 5 cm.

We need to find the length of AD.

In ΔACB and ΔADC, we note that

angle C = angle C

(common angle)

angle A = angle ADC = 90º

(AD is perpendicular to BC)

Therefore, ΔACB ~ ΔADC (by AA similarity criterion)

Therefore, by the property of similar triangles, we get

AD/AB = AC/BC

AD = (AC × AB)/BC

AD = (12×5)/13

AD = 60/13