Question

quadrilateral rstu is a rectangle, rt = 2w - 30, and su = 3w - 75. what is su?

Explanation:

Step1: Use the property of rectangle diagonals

In a rectangle, the diagonals are equal. So \(RT = SU\).
Given \(RT = 2w-30\) and \(SU = 3w - 75\), we set up the equation \(2w-30=3w - 75\).

Step2: Solve the equation for \(w\)

Subtract \(2w\) from both sides:
\(2w-30-2w=3w - 75-2w\)
\(- 30=w - 75\)
Add \(75\) to both sides:
\(-30 + 75=w-75 + 75\)
\(w = 45\)

Step3: Find the value of \(SU\)

Substitute \(w = 45\) into the formula for \(SU\):
\(SU=3w-75\)
\(SU=3\times45-75\)
\(SU = 135-75\)
\(SU=60\)

Answer:

\(60\)