In Fig, the area of rectangle $C D E F$ is twice the area of rectangle $A B C F$ . If $C D = 2 x + 2$ , calculate the length of $¯ ¯¯¯¯¯¯ ¯ A E$ , in terms of $x$ .

2 x + 3

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2 x + 4

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3 x + 1

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3 x + 2

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3 x + 3

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Solution

The correct option is E $3 x + 3$
Given, area of rectangle $C D F E$ is equal to twice the area of rectangle $A B C F$
$\Rightarrow C D \times C F = 2 \times B C \times C F$
$\Rightarrow B C = \frac{C D}{2} = x + 1$
Therefore, $A E = B D = B C + C D$
$= x + 1 + 2 x + 2$
$= 3 x + 3$

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