Question

WXYZ is a rhombus. WX=8x-5,WZ=6x+3 Find the perimeter.

Answer 1

To find the perimeter of a rhombus WXYZ where WX=8x-5 and WZ=6x+3, we first determine x by setting the expressions for WX and WZ equal, then calculate the length of one side and multiply by four to get the perimeter, which is 108 units.

Step-by-step explanation:

If WXYZ is a rhombus, and we are given that WX = 8x - 5 and WZ = 6x + 3, we can find the perimeter by first finding the value of x that makes WX and WZ equal since all sides of a rhombus are of equal length. This gives us:

8x - 5 = 6x + 3

By solving for x, we:

1. Subtract 6x from both sides: 2x - 5 = 3
2. Add 5 to both sides: 2x = 8
3. Divide both sides by 2: x = 4

Now we can substitute this value back into WX to get the length of one side of the rhombus:

WX = 8(4) - 5 = 32 - 5 = 27

Since each side of a rhombus is equal, the perimeter P is simply four times the length of one side.

P = 4 × 27 = 108

Therefore, the perimeter of rhombus WXYZ is 108 units.