Question

using the figure to the right and the following side lengths, find the value of x.
rs = 10(x - 4) + 2 and rt = 6(2x - 9)
the value of x is \boxed{}.

Explanation:

Step1: Identify RS = RT

From the figure, \( RS \) and \( RT \) are congruent (angle bisector or perpendicular bisector context), so set \( RS = RT \).
\( 10(x - 4) + 2 = 6(2x - 9) \)

Step2: Expand both sides

Expand left: \( 10x - 40 + 2 = 10x - 38 \)
Expand right: \( 12x - 54 \)
Equation: \( 10x - 38 = 12x - 54 \)

Step3: Solve for x

Subtract \( 10x \) from both sides: \( -38 = 2x - 54 \)
Add 54 to both sides: \( 16 = 2x \)
Divide by 2: \( x = 8 \)

Answer:

\( 8 \)