# In a ∆Abc, ∠A = 90°, Ab = 5 Cm and Ac = 12 Cm. If Ad ⊥ Bc, Then Ad = (A) 13 2 C M (B) 60 13 C M (C) 13 60 C M (D) 2 √ 15 13 C M - Mathematics

MCQ

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

#### Options

• $\frac{13}{2}cm$
• $\frac{60}{13}cm$
• $\frac{13}{60}cm$
• $\frac{2\sqrt{15}}{13}cm$

#### Solution

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

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.

Concept: Triangles Examples and Solutions
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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 7 Triangles
Q 42 | Page 136