Question

the quadrilateral shown is a rectangle. what is the measure of pr? (round to the nearest hundredth)
a 34.06
b 37.12
c 40.24
d 43.36

Explanation:

Step1: Recall rectangle property

In a rectangle, the diagonals are equal. So $PR = QS$. Also, we can use the Pythagorean theorem in right - triangle $PQR$ (or $PSR$) where the sides of the right - triangle are the length and width of the rectangle. Let $PQ = 33$ and $QR=17$.

Step2: Apply Pythagorean theorem

In right - triangle $PQR$, by the Pythagorean theorem $PR^{2}=PQ^{2}+QR^{2}$. Substitute $PQ = 33$ and $QR = 17$ into the formula: $PR=\sqrt{33^{2}+17^{2}}=\sqrt{1089 + 289}=\sqrt{1378}$.

Step3: Calculate the value

$\sqrt{1378}\approx37.12$.

Answer:

B. 37.12