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प्रश्न
In ∆ABC, ∠B = 90° and BD ⊥ AC.
- If CD = 10 cm and BD = 8 cm; find AD.
- If AC = 18 cm and AD = 6 cm; find BD.
- If AC = 9 cm and AB = 7 cm; find AD.
उत्तर
i. In ∆CDB,
∠1 + ∠2 + ∠3 = 180°
∠1 + ∠3 = 90° ...(1) (Since, ∠2 = 90°)
∠3 + ∠4 = 90° ...(2) (Since, ∠ABC = 90°)
From (1) and (2),
∠1 + ∠3 = ∠3 + ∠4
∠1 = ∠4
Also, ∠2 = ∠5 = 90°
∴ ∆CDB ~ ∆BDA ...(By AA similarity)
`=> (CD)/(BD) = (BD)/(AD)`
`=>` BD2 = AD × CD
`=>` (8)2 = AD × 10
`=>` AD = 6.4
Hence, AD = 6.4 cm
ii. Also, by similarity, we have:
`(BD)/(DA) = (CD)/(BD)`
BD2 = 6 × (18 – 6)
BD2 = 72
Hence, BD = 8.5 cm
iii. Clearly, ∆ADB ~ ∆ABC
`∴(AD)/(AB)=(AB)/(AC)`
`AD = (7 xx 7)/9`
= `(49)/9`
= `5 4/9`
Hence, `AD = 5 4/9 cm`
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