| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.94 |
| Score | 0% | 79% |
If the area of this square is 16, what is the length of one of the diagonals?
| 8\( \sqrt{2} \) | |
| 4\( \sqrt{2} \) | |
| 3\( \sqrt{2} \) | |
| 6\( \sqrt{2} \) |
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 = \( \sqrt{a} \) = \( \sqrt{16} \) = 4
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 = 42 + 42
c2 = 32
c = \( \sqrt{32} \) = \( \sqrt{16 x 2} \) = \( \sqrt{16} \) \( \sqrt{2} \)
c = 4\( \sqrt{2} \)
If side x = 5cm, side y = 8cm, and side z = 14cm what is the perimeter of this triangle?
| 39cm | |
| 33cm | |
| 27cm | |
| 31cm |
The perimeter of a triangle is the sum of the lengths of its sides:
p = x + y + z
p = 5cm + 8cm + 14cm = 27cm
If a = 9, b = 3, c = 7, and d = 7, what is the perimeter of this quadrilateral?
| 12 | |
| 16 | |
| 26 | |
| 20 |
Perimeter is equal to the sum of the four sides:
p = a + b + c + d
p = 9 + 3 + 7 + 7
p = 26
Which of the following expressions contains exactly two terms?
polynomial |
|
monomial |
|
binomial |
|
quadratic |
A monomial contains one term, a binomial contains two terms, and a polynomial contains more than two terms.
If angle a = 26° and angle b = 32° what is the length of angle c?
| 122° | |
| 54° | |
| 110° | |
| 68° |
The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 26° - 32° = 122°