Question

use the rhombus below to solve for $x$ and then find the length of $\overline{fg}$.

Explanation:

Step1: Use the property of a rhombus

In a rhombus, all sides are equal. So, \(x + 26=3x + 10\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides: \(26 = 2x+10\).
Subtract \(10\) from both sides: \(16 = 2x\).
Divide both sides by \(2\): \(x = 8\).

Step3: Find the length of \(FG\)

Substitute \(x = 8\) into \(3x + 10\).
\(FG=3\times8 + 10=24 + 10=34\).

Answer:

\(x = 8\), \(FG = 34\)