In parallelogram $A B C D$ , $A B = (3 x - 4)$ cm, $B C = (y - 1)$ cm, $C D = (y + 5)$ cm and $A D = (2 x + 5)$ cm. Find the ratio $A B : B C$ .

41 : 36

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35 : 41

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41 : 35

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36 : 41

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Solution

The correct option is D $41 : 35$
In parallelogram ABCD,
AB = CD
Substituting the given values, we get
$3 x - 4 = y - 1$
$3 x - y = 9$ --------- (1)
BC = AD
$y - 1 = 2 x + 5$
$2 x - y = - 6$ ---------- (2)
Now subtracting equation (2) from (1),
$x = 15 a n d y = 36$
Ratio of AB and BC is,
$\frac{A B}{B C}$ = $\frac{3 x - 4}{y - 1}$
Substituting values, we get
$∴$ $\frac{A B}{B C}$ = $\frac{41}{35}$

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