Advanced MathHardRectangle's diagonal from area and a relation
Advanced Math practice question
A rectangle's length is 3 units more than its width, and its area is 40 square units. What is the length of its diagonal? Round to the nearest tenth.
Answer: 9.4
w(w + 3) = 40 gives (w + 8)(w − 5) = 0, w = 5, length 8. Diagonal: √(25 + 64) = √89 ≈ 9.4.
Common wrong answers
- If you answered 8
- 8 is the length, not the diagonal.
- If you answered 13
- 13 adds the sides instead of using the Pythagorean theorem.
- If you answered 6.2
- 6.2 is √39, subtracting the squares.
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.