Question

in rectangle pqrs, sp = 7 and pr = 25. what is pq? pq =

Explanation:

Step1: Recall rectangle property

In a rectangle, the diagonals are equal and the angles are right - angled. So, in rectangle $PQRS$, $\angle SPQ = 90^{\circ}$ and $PR$ is a diagonal.

Step2: Apply Pythagorean theorem

By the Pythagorean theorem, in right - triangle $SPQ$, $PR^{2}=SP^{2}+PQ^{2}$. We know that $SP = 7$ and $PR = 25$. Then $PQ^{2}=PR^{2}-SP^{2}$.

Step3: Substitute values

$PQ^{2}=25^{2}-7^{2}=625 - 49=576$.

Step4: Find $PQ$

Taking the square root of both sides, $PQ=\sqrt{576}=24$.

Answer:

$24$