2x-4=4y-x=x+y

Question

We are given the three sides of a regular polygon as listed below, the top side is 2x-4, the right side is 4y-x and the bottom side is x+y.

2x-4
4y-x
x+y

Solve for x and y.

I keep getting different answers for x and y when using the substitution method.  Thank you for your time and assistance.

Answer 1

3-sided regular polygon=triangel...euqilateral triangel

forget all that gibberish with x's

Answer 2

If your polygon is regular, then all the sides are the same length.

So you can write: 2x-4=4y-x=x+y.

Turning these into single equations,

2x-4=4y-x ----- (1)

2x-4=x+y   ---- (2)

4y-x=x+y  ----- (3)

from (3), 2x = 3y, or x = 3y/2

substituting for x = 3y/2 into (1),

3y - 4 = 4y - 3y/2

9y/2 - 4y = 4

y/2 = 4

y = 8

x = 12

These values for x and y give the three expressions for the length of a side as,

l = 2x-4 = 24 - 4 = 20

l = 4y-x = 32 - 12 = 20

l = x+y = 12 + 8 = 20

The same value for l is gotten each time which confiorms our solution, i.e.

x = 12 y = 8