Question

what is st?
st =

Explanation:

Step1: Use the perpendicular bisector theorem

Since \(V\) is the mid - point of \(SU\) and \(TV\perp SU\), by the perpendicular bisector theorem, \(ST = UT\).
So, \(10x=x + 81\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides of the equation \(10x=x + 81\):
\(10x-x=x + 81-x\), which gives \(9x=81\).
Divide both sides by \(9\): \(x=\frac{81}{9}=9\).

Step3: Find the length of \(ST\)

Substitute \(x = 9\) into the expression for \(ST\) (\(ST = 10x\)).
\(ST=10\times9 = 90\).

Answer:

\(90\)