Question

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`

Answer 1

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)`