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?

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Solution

Q.
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

1 $x = \frac{a + b}{a y}$

2 $y = \frac{a x}{a + b}$

3 $x = \frac{a y}{a + b}$

4 $\frac{x}{y} = \frac{a}{b}$

Ans.
(3)

As $D E ∥ B C$

$∴$ $\frac{A E}{A C} = \frac{D E}{B C}$ $[From BPT]$

$\Rightarrow \frac{a}{a + b} = \frac{x}{y}$

$\Rightarrow x (a + b) = a y \Rightarrow x = \frac{a y}{a + b}$

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