Question

1. quadrilateral pqrs is a rectangle, qt = 10b + 23, and rt = 15b - 12. what is st?

Explanation:

Step1: Use the property of rectangle diagonals

In a rectangle, the diagonals are equal and bisect each other. So \(QT = RT\).

$$10b + 23=15b - 12$$

Step2: Solve for \(b\)

Subtract \(10b\) from both sides:

$$23 = 5b-12$$

Add \(12\) to both sides:

$$35 = 5b$$

Divide both sides by \(5\):

$$b = 7$$

Step3: Find \(QT\)

Substitute \(b = 7\) into \(QT=10b + 23\):

$$QT=10\times7 + 23=70 + 23=93$$

Step4: Use the property of diagonal bisection

Since \(ST = QT\) (diagonals bisect each other in a rectangle)

Answer:

\(93\)