Question

In rectangle PQRS, PQ = 18, PS = 14, and PR = 22.8. Diagonals PR and QS intersect at point T. What is the length of TQ?

A) 6
B) 8
C) 9.6
D) 11.4

Answer 1

TQ is 14.4 units long.

Step-by-step explanation:

To find the length of TQ, we can use the properties of rectangles and diagonals. We know that the diagonals of a rectangle bisect each other, meaning they divide each other into two equal parts.

Since PR is the longer diagonal, we can find its length by using the Pythagorean theorem: PR^2 = PQ^2 + QR^2. Plugging in the values, we get: 22.8^2 = 18^2 + QR^2. Solving for QR, we find QR = 14.4.

Since T is the intersection point of diagonals PR and QS, it divides QS into two equal parts. Therefore, TQ is also 14.4 units long.