Geometry and TrigonometryMedium45-45-90 triangle
Geometry and Trigonometry practice question
An isosceles right triangle has legs of length 7. What is the length of its hypotenuse?
- A. 7√2Correct
- B. 14
- C. 7
- D. 49
Answer: A. 7√2
The two legs are equal, so c² = 7² + 7² = 98 and c = √98 = √(49·2) = 7√2. In any 45-45-90 triangle the hypotenuse is the leg times √2.
Why the other answers are wrong
- B. 14
- 14 is 7 + 7. The legs' squares add, not the legs: √(49 + 49) = √98 = 7√2 ≈ 9.9, less than 14.
- C. 7
- The hypotenuse is always longer than a leg. It equals the leg only if the triangle collapses to a line.
- D. 49
- 49 is 7², one leg's square, not the hypotenuse. Two legs' squares add to 98, and the root of that is 7√2.
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