Question

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Answer 1

In parallelogram, opposite sides are equal.

Opposite sides are :-

AB and CD ; BC and AD

$\therefore$

AB = CD

(3x - 4) = (y + 5)

3x - 4 = y + 5

3x - y = 5 + 4

3x - y = 9 _____ (1)

Also,

BC = AD

(y - 1) = (2x + 5)

y - 1 = 2x + 5

2x - y = - 1 - 5

2x - y = - 6 _____(2)

Subtract (2) from (1), we get

(3x - y) - (2x - y) = (9) - (- 6)

3x - $\mathsf{\cancel{y}}$ - 2x + $\mathsf{\cancel{y}}$ = 9 + 6

x = 15

Put this value in (1), we get

3(15) - y = 9

45 - y = 9

y = 45 - 9

y = 36

AB = (3x - 4) = 3x - 4 = 3(15) - 4 = 45 - 4 = 41

BC = (y - 1) = y - 1 = 36 - 1 = 35

Ratio of AB and BC -

= AB / BC

= 41 / 35

= 41 : 35

Hence,

Value of x = 15

Value of y = 36

Ratio of AB : BC = 41 : 35

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