AbdurRakib
OG Q 2017 New Question(Book Question: 184)
Solution:We need to determine the side length of the larger (or circumscribed) square in centimeters.
Statement One Alone:Knowing the side length of the smaller (or inscribed) square is not sufficient to determine the side length of the larger square since we don’t know exactly where the vertices of the smaller square are located on the respective sides of the larger square.
Statement Two Alone:Knowing exactly the vertices of the smaller square are located on the respective sides of the larger square is not sufficient to determine the side length of the larger square since we don’t know the side length of the smaller square.
Statements One and Two Together:
We see that the vertices of the smaller square cut their respective sides of the larger square into two segments. If we let the shorter segment be x, then by statement two, the longer segment will be 2x (and notice that the side length of the larger square will then be 3x). By statement one, the side length of the smaller square is 10 cm; therefore, we can use the Pythagorean theorem on one of the unshaded triangles in the diagram to create the equation:
x^2 + (2x)^2 = 10^2
This allows us to solve for x and hence obtain the side length of the larger square. Both statements together are sufficient.
Answer: C