a In Fig, if AB || CD, find the value of x. A 15 B 12x-1 (2x + 4 4X-2 D In Fig. PA AR RC and on 11
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Step-by-step explanation:
(1) For Fig.a,
AB∥CD [ Given ]
∴ Quadrilateral ABCD is a trapezium.
∴
CO
AO
=
DO
BO
[ Diagonals of trapezium divides each other proportionally ]
⇒
4x−2
4
=
2x+4
x+1
⇒ 4(2x+4)=(x+1)(4x−2)
⇒ 8x+16=4x
2
−2x+4x−2
⇒ 4x
2
−6x−18=0
⇒ 2x
2
−3x−9=0
⇒ (x−3)(2x+3)=0
∴ x=3 or x=
2
−3
(2) For Fig.(b),
AB∥CD [ Given ]
∴ Quadrilateral ABCD is a trapezium.
∴
CO
AO
=
DO
BO
[ Diagonals of trapezium divides each other proportionally ]
⇒
5x−3
3x−1
=
6x−5
2x+1
⇒ (3x−1)(6x−5)=(2x+1)(5x−3)
⇒ 18x
2
−15x−6x+5=10x
2
−6x+5x−3
⇒ 8x
2
−20x+8=0
⇒ 2x
2
−5x+2=0
⇒ (x−2)(2x−1)=0
∴ x=2 or x=
2
1
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