PSAT Math Grid-Ins Question 42: Answer and Explanation
Question: 42
A right triangle has leg lengths of 18 and 24 and a hypotenuse of 15 n. What is the value of n ?
Correct Answer: 2
Explanation:
2
Difficulty: Medium
Category: Additional Topics in Math/Geometry
Getting to the Answer: You could use the Pythagorean theorem to solve this, but it will save valuable time on test day if you recognize that this question is testing your knowledge of Pythagorean triples. The triangle is a right triangle with leg lengths of 18 and 24, which, when divided by 6, are in the proportion 3:4. This means that the triangle is a scaled up 3:4:5 right triangle with a scale factor of 6. To keep the same proportion, the hypotenuse must be 5 × 6 = 30. For 15 n to equal 30, n must be 2.
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