SOLUTION: Rectangle ABCD is given Given: AB = x + y BC = x + 2y CD = 2x − y − 2 DA = 3x − 3y + 3 Find:x and y

Algebra ->  Formulas -> SOLUTION: Rectangle ABCD is given Given: AB = x + y BC = x + 2y CD = 2x − y − 2 DA = 3x − 3y + 3 Find:x and y      Log On


   

Question 1193117: Rectangle ABCD is given
Given:
AB = x + y
BC = x + 2y
CD = 2x − y − 2
DA = 3x − 3y + 3
Find:x and y
Found 2 solutions by greenestamps, MathLover1:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Opposite sides AB and CD are congruent; as are opposite sides BC and DA. Using the given information,

x%2By=2x-y-2
x%2B2y=3x-3y%2B3

Put each equation n Ax+By=C form....

x-2y=2
2x-5y=-3

My preference would be to solve using elimination. Multiply the first equation by -2 and add the two equations to eliminate x.

-2x%2B4y=-4
2x-5y=-3
-y=-7
y=7

Substitute y=7 in any earlier equation to solve for x. I leave that little bit to you.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Rectangle ABCD is given
Given:
AB+=+x+%2B+y
BC+=+x+%2B+2y
CD+=+2x+-y+-+2
DA+=+3x+-3y+%2B+3
Find: x and y

recall that opposite sides of a rectangle are equal in length, so
AB+=+CD and BC+=+DA+
then we have
x+%2B+y=+2x+-+y+-+2........solve for x
y+%2B+y%2B2=+2x+-+x+
x=2y%2B2+.........eq.1

x+%2B+2y=3x-+3y+%2B+3......solve for x
+3y+%2B+2y-3=3x+-x+
+5y-3=2x+
......multiply by 2
4y%2B4=+5y-3.......solve for y
3%2B4=+5y-4y
y=7

go to
x=2y%2B2+.........eq.1, substitute y
x=2%2A7%2B2+
x=16


now we can find the sides length:

AB+=+x+%2B+y=16%2B7=23
BC+=+x+%2B+2y=16%2B2%2A7=30
CD+=+2x+-y+-2=2%2A16-7-2=32-9=23
DA+=+3x+-3y+%2B+3=3%2A16-3%2A7%2B3=30