In a parallelogram ABCD, if $A B = 2 x + 5, C D = y + 1, A D = y + 5$ and $B C = 3 x - 4,$ then the ratio of $A B : B C$ is equal to

71 : 21

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12 : 11

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31 : 35

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4 : 7

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Solution

The correct option is C $31 : 35$

$A B = D C$ and $A D = B C$
[Both pairs of opposite sides of a parallelogram are equal]
$2 x + 5 = y + 1$
$\Rightarrow 2 x - y = - 4$ ........(1)
$y + 5 = 3 x - 4$
$\Rightarrow 3 x - y = 9$ ........(2)
On subtracting (1) from (2), we get,
$(3 x - y) - (2 x - y) = 9 - (- 4)$
$\Rightarrow x = 13$
So, $A B = 2 (13) + 5 = 26 + 5 = 31$
And, $B C = 3 (13) - 4 = 39 - 4 = 35$
Thus, the ratio of $A B : B C = 31 : 35$ .
Hence, the correct answer is option (c).

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In a parallelogram ABCD, if AB=2x+5,CD=y+1,AD=y+5 and BC=3x−4, then the ratio of AB:BC is equal to

In a parallelogram ABCD, if $A B = 2 x + 5, C D = y + 1, A D = y + 5$ and $B C = 3 x - 4,$ then the ratio of $A B : B C$ is equal to