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प्रश्न
In the figure given below, AB || EF || CD. If AB = 22.5 cm, EP = 7.5 cm, PC = 15 cm and DC = 27 cm.
Calculate :
- EF
- AC
उत्तर
In the given figure,
AB || EF || CD
AB = 22.5 cm, EP = 7.5 cm
PC = 15 cm and DC = 27 cm
To calculate:
- EF
- AC
In ΔDCP and ΔPEF
∠CPD = ∠EPF ...(Vertically opposite angles)
∠DCP = ∠PEF ...(Alternate angles)
∴ ΔDCP ∼ ΔPEF ...(AA axiom)
∴ `(DC)/(EF) = (CP)/(PE)`
`\implies 27/(EF) = 15/7.5`
`\implies EF = (27 xx 7.5)/15`
= `27/2`
= 13.5 cm
Similarly in ΔABC, EF || AB
∴ ΔCEF ∼ ΔACB
∴ `(CE)/(AC) = (EF)/(AB)`
`22.5/(AC) = 13.5/22.5`
`AC = (22.5 xx 22.5)/13.5`
= `(225 xx 225)/(135 xx 10 xx 10)`
= `375/10`
= 37.5 cm
Thus AC = 37.5 cm
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