Question

what is the value of c?
(options: 5 units, 4 units, 6 units, 7 units)
(image of a geometric figure with right angles at y and w, segments zy=3, wy=4, etc.)

Explanation:

Step1: Identify the right triangle

In triangle \( ZYW \), we have a right triangle with legs \( ZY = 3 \) and \( WY = 4 \), and hypotenuse \( c \) (which is \( ZW \)).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem states that for a right triangle with legs \( a \) and \( b \), and hypotenuse \( c \), \( c^2 = a^2 + b^2 \). Here, \( a = 3 \) and \( b = 4 \). So we calculate \( c^2 = 3^2 + 4^2 \).

Step3: Calculate the values

First, \( 3^2 = 9 \) and \( 4^2 = 16 \). Then, \( c^2 = 9 + 16 = 25 \). Taking the square root of both sides, \( c = \sqrt{25} = 5 \).

Answer:

5 units