Question

find the value of x, y, and z, in the rhombus below. 8 -x - 6 -5y + 3 -8z - 8 answer attempt 1 out of 2 x = y = z =

Explanation:

Step1: Use the property of rhombus sides

In a rhombus, all sides are equal. So, we can set up equations:

• For side \(8\) and \(-x - 6\): \(8=-x - 6\)
• For side \(8\) and \(-5y+3\): \(8=-5y + 3\)
• For side \(8\) and \(-8z-8\): \(8=-8z - 8\)

Step2: Solve for \(x\)

From \(8=-x - 6\), add \(x\) to both sides: \(x + 8=-6\). Then subtract \(8\) from both sides: \(x=-6 - 8=-14\)

Step3: Solve for \(y\)

From \(8=-5y + 3\), subtract \(3\) from both sides: \(5=-5y\). Divide both sides by \(-5\): \(y = - 1\)

Step4: Solve for \(z\)

From \(8=-8z - 8\), add \(8\) to both sides: \(16=-8z\). Divide both sides by \(-8\): \(z=-2\)

Answer:

\(x=-14\), \(y = - 1\), \(z=-2\)