# In the figure above, what is the value of…

## Solution:

We need to determine the value of z in the following diagram:

Note that z is equal to the length of the rectangle and the base of the triangle. If we let the base of the triangle = b, z = b + y.

**Statement One Alone:**

x = y = 1

Although we know that x = 1, we do not know the value of b or the base of the triangle. Statement one alone is not sufficient to answer the question.

**Statement Two Alone:**

w = 2

Knowing only the value of w does not allow us to determine z. Statement two alone is not sufficient to answer the question.

**Statements One and Two Together:**

Using the information from statements one and two, we know that x = y = 1 and w = 2, and we can determine b using the Pythagorean theorem.

x^2 + b^2 = w^2

1^2 + b^2 = 2^2

1 + b^2 = 4

b^2 = 3

b = √3

Thus, z = y + b = 1 + √3.

**Answer: C**