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