Advanced MathHardNumber of sides from a count of diagonals
Advanced Math practice question
A polygon with n sides has n(n − 3)/2 diagonals. How many sides does a polygon with 20 diagonals have?
Answer: 8
n(n − 3)/2 = 20 → n² − 3n − 40 = 0 → (n − 8)(n + 5) = 0 → n = 8.
Common wrong answers
- If you answered 5
- 5 gives 5(2)/2 = 5 diagonals.
- If you answered 10
- 10 gives 10(7)/2 = 35 diagonals.
- If you answered -5
- −5 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.