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In a ∆Abc, ∠A = 90°, Ab = 5 Cm and Ac = 12 Cm. If Ad ⊥ Bc, Then Ad = 13 2 C M 60 13 C M 13 60 C M 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

  • \[\frac{13}{2}cm\]

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

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)
 
\[\angle A = \angle ADC = 90^\circ\]
∴ ∆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 13 | Page 132
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