Question

In triangle PQR, angle Q = 90 degrees, and segment SQ is perpendicular to the hypotenuse PR. If PS = 16 cm and SR = 9 cm, then what is the length of QS? a) 15 cm b) 12 cm c) 25 cm d) 20 cm

Answer 1

In triangle PQR, with a right angle at Q and a perpendicular segment SQ, the length of QS is 9 cm.

Step-by-step explanation:

In triangle PQR, angle Q is a right angle, and segment SQ is perpendicular to the hypotenuse PR. Since triangle QSR is similar to triangle PQR, we can use the property of similar triangles to find the length of QS.

Using the similarity ratio, we can write:

QS/PQ = SR/PR

Substituting the given values:

QS/25 = 9/25

QS = 9

Thus, the length of QS is 9 cm.

Learn more about Triangle Properties