Question

what is the value of c?
○ 4 units
○ 5 units
○ 6 units
○ 7 units
(image shows a right triangle wxz with right angle at w, and a segment wy perpendicular to xz with wy=4, zy=3, and right angles at w and y)

Explanation:

Step1: Recall Geometric Mean Theorem

In a right triangle, the altitude to the hypotenuse relates the segments of the hypotenuse and the legs. For right triangle \( \triangle WZX \) with altitude \( WY \) to hypotenuse \( ZX \), the geometric mean theorem states \( c^2 = ZY \times ZX \), but also, in right triangle \( \triangle WYZ \), \( c \) is the hypotenuse, and \( ZY = 3 \), \( WY = 4 \). Wait, actually, \( \triangle WYZ \) is a right triangle with legs 3 and 4, so by Pythagorean theorem: \( c^2 = 3^2 + 4^2 \).

Step2: Calculate \( c \)

Compute \( 3^2 + 4^2 = 9 + 16 = 25 \). Then \( c = \sqrt{25} = 5 \).

Answer:

5 units (the option with "5 units")