Question

find the value of ( x ), ( y ), and ( z ), in the rhombus below.

(image of a rhombus with side labels: -8x - 10 (top), 46 (right), z + 4 (bottom), -y + 3 (left))

answer attempt 1 out of 2

( x = square ) ( y = square ) ( z = square )

Explanation:

Step1: Recall rhombus property (all sides equal)

In a rhombus, all four sides are of equal length. So, we can set up equations by equating the expressions for the sides.

Step2: Solve for \( x \)

One side is \( -8x - 10 \) and another is \( 46 \). So, \( -8x - 10 = 46 \).
Add \( 10 \) to both sides: \( -8x = 46 + 10 = 56 \).
Divide by \( -8 \): \( x = \frac{56}{-8} = -7 \).

Step3: Solve for \( y \)

One side is \( -y + 3 \) and another is \( 46 \). So, \( -y + 3 = 46 \).
Subtract \( 3 \) from both sides: \( -y = 46 - 3 = 43 \).
Multiply by \( -1 \): \( y = -43 \).

Step4: Solve for \( z \)

One side is \( z + 4 \) and another is \( 46 \). So, \( z + 4 = 46 \).
Subtract \( 4 \) from both sides: \( z = 46 - 4 = 42 \).

Answer:

\( x = -7 \), \( y = -43 \), \( z = 42 \)