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 =