Calculate the missing side of the triangle below.

• A. $2\sqrt{5}$
• B. $2$
• C. $5$
• D. $2\sqrt{3}$

Answer: (A)

Verified step by step guidance

1. Identify the type of triangle: The given triangle is a right triangle with legs of lengths 4 and 2, and hypotenuse z.
2. Apply 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 legs of the triangle.
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 and 2^2, which are 16 and 4, respectively.
5. Add the squares of the legs: Add 16 and 4 to get the value of z^2, which is 20. Then, take the square root of both sides to solve for z, giving z = \(\sqrt{20}\).