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 (since they are corresponding segments in a congruent angle or right - angle context, so \( RS = RT \)).
Given \( RS = 10(x - 4)+2 \) and \( RT=6(2x - 9) \), we set up the equation:
\( 10(x - 4)+2=6(2x - 9) \)

Step2: Expand both sides

Expand the left - hand side: \( 10(x - 4)+2=10x-40 + 2=10x-38 \)
Expand the right - hand side: \( 6(2x - 9)=12x-54 \)
So the equation becomes \( 10x-38 = 12x-54 \)

Step3: Solve for x

Subtract \( 10x \) from both sides:
\( 10x-38-10x=12x - 54-10x \)
\( - 38 = 2x-54 \)
Add 54 to both sides:
\( -38 + 54=2x-54 + 54 \)
\( 16 = 2x \)
Divide both sides by 2:
\( x=\frac{16}{2}=8 \)

Answer:

\( 8 \)