Question

in the figure below, points s, t, and u are the midpoints of the sides of δpqr. suppose pr = 70, pq = 74, and su = 12. find the following lengths. qr = \square, qt = \square, st = \square

Explanation:

Step1: Apply Midsegment Theorem to SU

The midsegment $SU$ is half of $QR$.
$QR = 2 \times SU$
$QR = 2 \times 12 = 24$

Step2: Find QT (midpoint of QR)

$T$ is the midpoint of $QR$, so $QT = \frac{QR}{2}$.
$QT = \frac{24}{2} = 12$

Step3: Apply Midsegment Theorem to ST

The midsegment $ST$ is half of $PR$.
$ST = \frac{PR}{2}$
$ST = \frac{70}{2} = 35$

Answer:

$QR = 24$
$QT = 12$
$ST = 35$