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प्रश्न
In the given figure, PQ || AB; CQ = 4.8 cm QB = 3.6 cm and AB = 6.3 cm. Find :
- `(CP)/(PA)`
- PQ
- If AP = x, then the value of AC in terms of x.
उत्तर
i. In ΔCPQ and ΔCAB,
∠PCQ = ∠ACB ...(Since PQ || AB, so the angles are corresponding angles)
∠C = ∠C ...(Common angle)
∴ ΔCPQ ∼ ΔCAB ...(AA criterion for similarity)
`=> (CP)/(PA) = (CQ)/(QB)`
`=> (CP)/(PA) = (4.8)/(3.6) = (48)/(36) = 4/3`
So, `(CP)/(PA) = 4/3`
ii. In ΔCPQ and ΔCAB,
∠PCQ = ∠ACB ...(Since PQ || AB, so the angles are corresponding angles)
∠C = ∠C ...(Common angle)
∴ ΔCPQ ∼ ΔCAB ...(AA criterion for similarity)
`=> (PQ)/(AB) = (CQ)/(CB)`
`=> (PQ)/(6.3) = (4.8)/(8.4) `
So, PQ = 3.6
iii. In ΔCPQ and ΔCAB,
∠PCQ = ∠ACB ...(Since PQ || AB, so the angles are corresponding angles)
∠C = ∠C ...(Common angle)
∴ ΔCPQ ∼ ΔCAB ...(AA criterion for similarity)
`=> (CP)/(AC) = (CQ)/(CB)`
`=> (CP)/(AC) = (4.8)/(8.4) = 4/7 `
So, if AC is 7 parts, and CP is 4 parts, then PA is 3 parts.
Given, AP = x
or 3 parts = x
`=>` 1 part = `x/3`
`=>` 7 parts = `(7x)/3`
Hence, AC = `(7x)/3`
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