| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.73 |
| Score | 0% | 75% |
If the area of this square is 9, what is the length of one of the diagonals?
| 6\( \sqrt{2} \) | |
| 9\( \sqrt{2} \) | |
| 2\( \sqrt{2} \) | |
| 3\( \sqrt{2} \) |
To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:
a = s2
so the length of one side of the square is:
s = \( \sqrt{a} \) = \( \sqrt{9} \) = 3
The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:
c2 = a2 + b2
c2 = 32 + 32
c2 = 18
c = \( \sqrt{18} \) = \( \sqrt{9 x 2} \) = \( \sqrt{9} \) \( \sqrt{2} \)
c = 3\( \sqrt{2} \)
If side x = 5cm, side y = 6cm, and side z = 15cm what is the perimeter of this triangle?
| 26cm | |
| 29cm | |
| 33cm | |
| 27cm |
The perimeter of a triangle is the sum of the lengths of its sides:
p = x + y + z
p = 5cm + 6cm + 15cm = 26cm
If angle a = 30° and angle b = 51° what is the length of angle c?
| 57° | |
| 123° | |
| 99° | |
| 94° |
The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 30° - 51° = 99°
Breaking apart a quadratic expression into a pair of binomials is called:
squaring |
|
factoring |
|
normalizing |
|
deconstructing |
To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.
If AD = 21 and BD = 14, AB = ?
| 1 | |
| 19 | |
| 15 | |
| 7 |
The entire length of this line is represented by AD which is AB + BD:
AD = AB + BD
Solving for AB:AB = AD - BD