Pythagorean Theorem
Question
Answer choices
- 9
- 10
- 11
- 2
- 14
B Correct answer: B) 10
Set up the problem carefully before computing. For any right triangle, leg² + leg² = hypotenuse². Memorize 3-4-5, 5-12-13, 8-15-17, 7-24-25.
Carry the arithmetic through one step at a time, double-checking signs and units. The ACT writes wrong answers to catch the most common slips, so an answer that "looks right" without verification is risky.
Plug the answer back into the original expression as a sanity check whenever the problem allows. If the substitution does not balance, you have made an arithmetic mistake earlier in the work.
The underlying rule
By the Pythagorean theorem, hypotenuse² = 6² + 8² = 36 + 64 = 100. So hypotenuse = √100 = 10.
Why each wrong answer is wrong
- A) 9: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- C) 11: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- D) 2: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- E) 14: A common arithmetic or sign error leads to this value; carefully redo the calculation.
Study tip
Memorize the four Pythagorean triples that appear constantly: 3-4-5, 5-12-13, 8-15-17, 7-24-25 — and their multiples (6-8-10, 9-12-15).
More Medium Plane Geometry
- Area of a TriangleA triangle has base 6 cm and height 5 cm. What is its area in square centimeters?
- Area of a CircleWhat is the area of a circle with radius 4? Express your answer in terms of π.
- Pythagorean TheoremA right triangle has legs of length 8 and 15. What is the length of its hypotenuse?
- Perimeter of a RectangleA rectangle has length 9 and width 3. What is its perimeter?
- Area of a TriangleA triangle has base 12 cm and height 5 cm. What is its area in square centimeters?