SOLUTION: In the rectangle PQRS , PQ=(4x-y)cm , QR= (x+4)cm ,RS=(2x+y+6)cm, SP= 2ycm, Find x and y

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Question 1043322: In the rectangle PQRS , PQ=(4x-y)cm , QR= (x+4)cm ,RS=(2x+y+6)cm, SP= 2ycm, Find x and y
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In the rectangle PQRS , PQ=(4x-y)cm , QR= (x+4)cm ,RS=(2x+y+6)cm, SP= 2ycm, Find x and y
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In a rectangle, the opposite sides are congruent and have equal lengths. Therefore

4x - y = 2x + y + 6,   (1)   ( |PQ| = |RS| )
x + 4 = 2y.            (2)   ( |QR| = }SP| )

To solve it, express x = 2y - 4 from (2) and substitute it into (1). You will get

4(2y-4) - y = 2(2y-4) + y + 6.

Simplify it:

2y = 14,   --->  y = 7.

Then x = 2y - 4 = 10.

Answer. x = 10, y = 7.