Question

In a ∆ABC, ∠A = 90°, AB = 5 cm and AC = 12 cm. If AD ⊥ BC, then AD =

Options

• \[\frac{13}{2}cm\]
• \[\frac{60}{13}cm\]
• \[\frac{13}{60}cm\]
• \[\frac{2\sqrt{15}}{13}cm\]

Answer 1

Given: In ΔABC, `∠ A = 90^o` AD ⊥ BC, AC = 12cm, and AB = 5cm.

To find: AD

We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.

In ∆ACB and ∆ADC,

\[\angle C = \angle C\]        (Common)

\[\angle A = \angle ADC = 90^o\]

∴ ∆ACB ∼ ∆ADC     (AA Similarity)

`(AD)/(AB)=(AC)/(BC)`

`AD=(ABxxAC)/(BC)`

`AD=(12xx5)/13`

`AD= 60/13`

We got the result as `b`.