SOLUTION: Find the measure of x and y: Have a parrallegram bisected into 4 quadrants: 1 on top is 2y-2, one on right is 2y, one on bottom is x+y, one on left is 3x. If I'd set up equation I

Click here to see ALL problems on Parallelograms

Question 1113713: Find the measure of x and y:
Have a parrallegram bisected into 4 quadrants: 1 on top is 2y-2, one on right is 2y, one on bottom is x+y, one on left is 3x. If I'd set up equation I'd have an x and y on the same problem..how do I do??
2y-2=x+y
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
you break the parallelogram into 4 quadrants by drawing two diagonals to connect opposite corners of the parallelogram.

this creates two sets of congruent triangles.

the top triangle is congruent to the bottom triangle.
the left triangle is congruent to the right triangle.

they are congruent by SSS.

that's why you get 2y-2 = x+y and 3x = 2y

you have 2 equations that need to be solved simultaneously because the same value of x and the same value of y applies to both equations.

start with:

2y-2 = x+y
3x = 2y

use either equation to solve for x or y.

i chose the second equation to solve for x.

i got x = (2/3) * y

i then replaced x with (2/3) * y in the first equation to get:

2y-2 = (2/3) * y + y

this is one equation in one variable that can give you a unique solution.

combine like terms to get 2y-2 = 5/3 * y

subtract 5/3 * y from both sides of the equation and add 2 to both sides of the equation to get:

2y - 5/3 * y = 2

multiply both sides of the equation by 3 to get:

6y - 5y = 6

solve for y to get y = 6

in the second equation, replace y with 6 to get:

3x = 2y becomes 3x= 12.

solve for x to get x = 4

that's your solution.

x = 4 and y = 6

3x = 2y becomes 3*4 = 2*6 which becomes 6 = 6 which is true.

2y-2 = x+y becomes 2*6-2 = 4+6 becomes 12-2 = 10 which becomes 10 = 10 which is true.

solution is confirmed to be good.

presumably the area of each triangleis equa