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प्रश्न
In the given figure, DE ∥ BC, AE = a units, EC = b units, DE = x units and BC = y units. Which of the following is true?
विकल्प
x = `(a + b)/(ay)`
y = `(ax)/(a + b)`
x = `(ay)/(a + b)`
`x/y = a/b`
उत्तर
x = `(ay)/(a + b)`
Explanation:
In ΔADE and ΔABC
ΔADE = ΔABC ......(Corresponding angle)
∠A = ∠A ......(Common)
∴ ΔADE ∼ ΔABC ....(AA similarity criterion)
Now, `(AD)/(AB) = (DE)/(BC) = (AE)/(AC)`
`(DE)/(BC) = (AE)/(AC)`
`x/y = a/(a + b)`
x = `(ay)/(a + b)`
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