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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