ISEE Word Problems Question 218: Answer and Explanation
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Question: 218
6. A square inscribed in a square is shown.
In terms of x, what is the length of line segment m?
- A. 5x2
- B. 13x2
- C. x
- D. x
Correct Answer: D
Explanation:
The answer is D
As the outer figure is a square, each vertex is 90° and, thus, part of a right triangle. The four right triangles are identical, so set up the Pythagorean theorem to find m: (2x)2 + (3x)2 = m2. Distribute the exponents and combine like terms: 13x2 = m2. Take the square root of both sides m = x.
Plug in a value for x, such as 2. The sides of the outer square are now divided into segments of length 4 and 6. As the triangles are right triangles, use the Pythagorean theorem to find m: 42 + 62 = m2 = 52. Thus m =
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