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# If the equation of the opposite sides of a parallelogram are 4x + 5y =

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Intern
Joined: 21 May 2016
Posts: 26
If the equation of the opposite sides of a parallelogram are 4x + 5y =  [#permalink]

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30 Jul 2018, 12:15
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Difficulty:

45% (medium)

Question Stats:

58% (01:17) correct 42% (02:25) wrong based on 24 sessions

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If the equation of the opposite sides of a parallelogram are 4x + 5y = 20 and ax - 2y = 9, what is the value of a?

A. 4/5
B. -8/5
C. 8/5
D. -2/5
E. 5/2
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Joined: 24 Aug 2016
Posts: 401
Concentration: Entrepreneurship, Operations
GMAT 1: 630 Q48 V28
Re: If the equation of the opposite sides of a parallelogram are 4x + 5y =  [#permalink]

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30 Jul 2018, 12:28
ankit2601 wrote:
if the equation of the opposite sides of a parallelogram are 4x+5y=20 and ax-2y=9, what is the value of a?
A. 4/5
B. -8/5
C. 8/5
D. -2/5
E. 5/2

Equation of straight line : y=mx+c where M is the slope

Line 01 : 4x+5y=20 or y= -$$\frac{4}{5}$$x + 4 Hence Slope= -$$\frac{4}{5}$$

Line 02 : ax-2y=9 y= $$\frac{a}{2}$$x - 9/2 Hence Slope= $$\frac{a}{2}$$

As Line 01 & 02 are the opposites sides of a parallelogram... they are parallel to each other. Hence they have equal slope.
Hence, -$$\frac{4}{5}$$=$$\frac{a}{2}$$
Hence a = -$$\frac{8}{5}$$..........................................Answer B
_________________

Please let me know if I am going in wrong direction.
Thanks in appreciation.

Re: If the equation of the opposite sides of a parallelogram are 4x + 5y = &nbs [#permalink] 30 Jul 2018, 12:28
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