Question

find the value of x, y, and z, in the rhombus below.
(image of a rhombus with sides labeled: -2y - 7, 8x - 5, 3, 7z - 4)
answer attempt 1 out of 2
x = y = z =
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Explanation:

Step1: Recall rhombus side property

In a rhombus, all four sides are equal in length. So, the side labeled \(8x - 5\) should equal the side labeled \(3\), the side labeled \(-2y - 7\) should equal \(3\), and the side labeled \(7z - 4\) should equal \(3\).

Step2: Solve for \(x\)

Set \(8x - 5 = 3\).
Add \(5\) to both sides: \(8x = 3 + 5 = 8\).
Divide both sides by \(8\): \(x=\frac{8}{8}=1\).

Step3: Solve for \(y\)

Set \(-2y - 7 = 3\).
Add \(7\) to both sides: \(-2y = 3 + 7 = 10\).
Divide both sides by \(-2\): \(y=\frac{10}{-2}=-5\).

Step4: Solve for \(z\)

Set \(7z - 4 = 3\).
Add \(4\) to both sides: \(7z = 3 + 4 = 7\).
Divide both sides by \(7\): \(z=\frac{7}{7}=1\).

Answer:

\(x = 1\), \(y = -5\), \(z = 1\)