Question

1. solve for x & find sr.

10x - 3
3x + 39
x =
sr =

Explanation:

Step1: Assume equal - length segments

If the two segments from the point \(P\) to the vertical line are congruent (assuming some congruence property like angle - bisector or similar triangles property), we can set up the equation \(10x - 3=3x + 39\).

Step2: Solve the linear equation for \(x\)

Subtract \(3x\) from both sides: \(10x-3x - 3=3x-3x + 39\), which simplifies to \(7x-3 = 39\). Then add 3 to both sides: \(7x-3 + 3=39 + 3\), getting \(7x=42\). Divide both sides by 7: \(x=\frac{42}{7}=6\).

Step3: Find the length of \(SR\)

Since \(SR = 3x + 39\), substitute \(x = 6\) into the expression. \(SR=3\times6+39=18 + 39=57\).

Answer:

\(x = 6\)
\(SR = 57\)