Question

quadrilateral pqrs is a rectangle, pr = t + 24, and qs = 4t. what is qs? qs = \boxed{}

Explanation:

Step1: Set diagonals equal

In a rectangle, diagonals are congruent, so $PR = QS$. Substitute the given expressions:
$t + 24 = 4t$

Step2: Solve for $t$

Subtract $t$ from both sides:
$24 = 3t$
Divide both sides by 3:
$t = \frac{24}{3} = 8$

Step3: Calculate length of $QS$

Substitute $t=8$ into $QS=4t$:
$QS = 4 \times 8$

Answer:

32