Advanced MathHardLegs of a right triangle from the hypotenuse and a relation
Advanced Math practice question
A right triangle has a hypotenuse of 10 units, and one leg is 2 units longer than the other. What is the length of the shorter leg?
Answer: 6
s² + (s + 2)² = 100 gives 2s² + 4s − 96 = 0, s² + 2s − 48 = (s + 8)(s − 6) = 0, so s = 6.
Common wrong answers
- If you answered 5
- 5 comes from a slip in halving: s² + 2s = 48, not 24.
- If you answered 8
- 8 is the longer leg.
- If you answered -8
- −8 is the rejected negative root.
More Advanced Math questions
- Hard
A population of bacteria doubles every 3 hours. If it starts at 500, which function models the population P af… - Hard
How many real solutions does x² + 4x + 5 = 0 have? - Hard
A car worth $20,000 loses 15% of its value each year. What is its value after 2 years? - Hard
An investment of $1,000 grows at 6% per year, compounded annually. Which expression gives its value after t ye… - Hard
If f(x) = x² − 1 and g(x) = x + 2, what is g(f(3))? - Hard
The parabola y = x² − 8x + 12 crosses the x-axis at two points. What is the x-coordinate of the vertex?
Not affiliated with the College Board. SAT is a trademark of the College Board.