Question

41 quadrilateral stuv is a rectangle, su = 2p + 60, and tv = 3p + 57. what is tv?

Explanation:

Step1: Use the property of rectangle diagonals

In a rectangle, the diagonals are equal. So \(SU = TV\).
Given \(SU=2p + 60\) and \(TV = 3p+57\), we set up the equation \(2p + 60=3p + 57\).

Step2: Solve the equation for \(p\)

Subtract \(2p\) from both sides:
\(2p+60-2p=3p + 57-2p\)
\(60=p + 57\)
Subtract \(57\) from both sides:
\(p=60 - 57\)
\(p = 3\)

Step3: Find the value of \(TV\)

Substitute \(p = 3\) into the formula for \(TV\). Since \(TV=3p + 57\), then \(TV=3\times3+57\)
\(TV=9 + 57\)
\(TV=66\)

Answer:

\(66\)