Answer:
PQ = 13 cm
Step-by-step explanation:
You need to use the Pythagorean Theorem twice.
On the base of the cuboid, mark the point opposite P, point A. Point A is vertically below point Q. Now draw a segment from point P to point A.
The distance from point P to point A can be found using the Pythagorean Theorem.
(3 cm)^2 + (4 cm)^2 = (PA)^2
9 cm^2 + 16 cm^2 = (PA)^2
25 cm^2 = (PA)^2
PA = 5 cm
Segment PA is a side of triangle PAQ. Angle PAQ is a right angle. Sides PA and AQ are legs of the right triangle, and side PQ is the hypotenuse. Now we use the Pythagorean Theorem again.
(PA)^2 + (AQ)^2 = (PQ)^2
(5 cm)^2 + (12 cm)^2 = (PQ)^2
25 cm^2 + 144 cm^2 = (PQ)^2
169 cm^2 = (PQ)^2
PQ = 13 cm
