| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.41 |
| Score | 0% | 68% |
If side a = 5, side b = 1, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{20} \) | |
| \( \sqrt{68} \) | |
| \( \sqrt{26} \) | |
| 10 |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 52 + 12
c2 = 25 + 1
c2 = 26
c = \( \sqrt{26} \)
Solve for c:
c2 + 10c + 24 = 0
| -4 or -6 | |
| -7 or -9 | |
| 2 or -6 | |
| 5 or -4 |
The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:
c2 + 10c + 24 = 0
(c + 4)(c + 6) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (c + 4) or (c + 6) must equal zero:
If (c + 4) = 0, c must equal -4
If (c + 6) = 0, c must equal -6
So the solution is that c = -4 or -6
What is the circumference of a circle with a radius of 8?
| 30π | |
| 24π | |
| 5π | |
| 16π |
The formula for circumference is circle diameter x π. Circle diameter is 2 x radius:
c = πd
c = π(2 * r)
c = π(2 * 8)
c = 16π
If side x = 6cm, side y = 9cm, and side z = 7cm what is the perimeter of this triangle?
| 22cm | |
| 33cm | |
| 29cm | |
| 25cm |
The perimeter of a triangle is the sum of the lengths of its sides:
p = x + y + z
p = 6cm + 9cm + 7cm = 22cm
Which of the following is not true about both rectangles and squares?
all interior angles are right angles |
|
the perimeter is the sum of the lengths of all four sides |
|
the area is length x width |
|
the lengths of all sides are equal |
A rectangle is a parallelogram containing four right angles. Opposite sides (a = c, b = d) are equal and the perimeter is the sum of the lengths of all sides (a + b + c + d) or, comonly, 2 x length x width. The area of a rectangle is length x width. A square is a rectangle with four equal length sides. The perimeter of a square is 4 x length of one side (4s) and the area is the length of one side squared (s2).