In a parallelogram ABCD, if AB=2x+5,CD=y+1,AD=y+5 and BC=3x−4, what is the ratio of AB and BC?
12:11
4:7
31:35
71:21
A
71:21
B
12:11
C
31:35
D
4:7
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Solution
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In parallelogram, opposite sides are parallel and equal ∴AB=CD and AD=BC ⇒2x+5=y+1⟶1 ⇒3x−4=y+5⟶2 Equation 2-equation 1 (3x−2x)−4−5=0+4 x=13 Put value of x in 1 2(13)+5−1=y y=30 ABBC=2x+53x−4=2(13)+53(13)−4 ABBC=3135 ∴AB:BC=31:35
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