ISEE Mathematics Achievement Question 19: Answer and Explanation

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Question: 19

5. Use the diagram below to answer the question.

Given the lengths of the base and diagonal of the rectangle above, what is the length of height h, in terms of s?

  • A. s
  • B. s
  • C. 3s
  • D. 3s2

Correct Answer: A

Explanation:

A

Set up an equation using the Pythagorean theorem: h2 + s2 = (2s)2. Distribute the exponent on the right and subtract s2 from both sides: h2 = 3s2. Take the square root of both sides: h = s.

Plug in a value for s such as s = 2, and set up an equation using the Pythagorean theorem: h2 + 22 = 42. Apply the exponents and subtract 4 from both sides: h2 = 12. Take the square root of both sides and simplify the value under the square root sign: h = . Only choice

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