Calculate the missing side of the triangle below.

• A. $2\sqrt5$
• B. $2$
• C. $5$
• D. $2\sqrt3$

Answer: (A)

Verified step by step guidance

1. Identify the type of triangle: The image shows a right triangle with legs of lengths 4 and 2, and the hypotenuse labeled as z.
2. Recall the Pythagorean theorem: In a right triangle, the square of the hypotenuse (z) is equal to the sum of the squares of the other two sides. The formula is: z^2 = a^2 + b^2, where a and b are the lengths of the legs.
3. Substitute the known values into the Pythagorean theorem: Here, a = 4 and b = 2. So, the equation becomes: z^2 = 4^2 + 2^2.
4. Calculate the squares of the legs: Compute 4^2 = 16 and 2^2 = 4.
5. Add the squares of the legs: Add the results from the previous step to find z^2 = 16 + 4 = 20. To find z, take the square root of both sides: z = √20.