Question

find the value of x, y, and z, in the rhombus below.
answer attempt 1 out of 2
x =
y =
z =

Explanation:

Step1: Use the property of a rhombus (all sides are equal)

Since all sides of a rhombus are equal, we have the following equations:

• For the side with expressions \(-3x - 3\) and \(9\): \(-3x-3=9\)
• For the side with expressions \(8y - 7\) and \(9\): \(8y-7 = 9\)
• For the side with expressions \(-2z + 5\) and \(9\): \(-2z+5=9\)

Step2: Solve the equation for \(x\)

Starting with \(-3x-3 = 9\).
Add \(3\) to both sides: \(-3x=9 + 3\), so \(-3x=12\).
Divide both sides by \(-3\): \(x=\frac{12}{-3}=- 4\)

Step3: Solve the equation for \(y\)

Starting with \(8y-7 = 9\).
Add \(7\) to both sides: \(8y=9 + 7\), so \(8y=16\).
Divide both sides by \(8\): \(y=\frac{16}{8}=2\)

Step4: Solve the equation for \(z\)

Starting with \(-2z+5 = 9\).
Subtract \(5\) from both sides: \(-2z=9 - 5\), so \(-2z=4\).
Divide both sides by \(-2\): \(z=\frac{4}{-2}=-2\)

Answer:

\(x=-4\), \(y = 2\), \(z=-2\)