Question

Triangle X Y Z is shown. Angle Z W X is a right angle. An altitude is drawn from point W to point Y on side Z X to form a right angle. The length of W Y is 4, the length of Y X is a, the length of Z Y is 3, the length of Z W is c, and the length of W X is b.
What is the value of a?

5 units
5 and one-third units
6 and two-thirds units
7 units

Answer 1

WY is the altitude to the hypotenuse in right triangle ZWX, so WY^2 = ZY·YX. Thus 4^2 = 3·a ⇒ 16 = 3a ⇒ a = 16/3 = 5 1/3.

Answer: 5 and one-third units.