| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.81 |
| Score | 0% | 56% |
For this diagram, the Pythagorean theorem states that b2 = ?
c2 - a2 |
|
c - a |
|
a2 - c2 |
|
c2 + a2 |
The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c2) is equal to the sum of the two perpendicular sides squared (a2 + b2): c2 = a2 + b2 or, solved for c, \(c = \sqrt{a + b}\)
If side a = 4, side b = 5, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{113} \) | |
| \( \sqrt{5} \) | |
| \( \sqrt{89} \) | |
| \( \sqrt{41} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 42 + 52
c2 = 16 + 25
c2 = 41
c = \( \sqrt{41} \)
If the base of this triangle is 4 and the height is 3, what is the area?
| 60 | |
| 6 | |
| 66 | |
| 67\(\frac{1}{2}\) |
The area of a triangle is equal to ½ base x height:
a = ½bh
a = ½ x 4 x 3 = \( \frac{12}{2} \) = 6
A trapezoid is a quadrilateral with one set of __________ sides.
equal length |
|
right angle |
|
parallel |
|
equal angle |
A trapezoid is a quadrilateral with one set of parallel sides.
Solve for x:
2x + 4 > \( \frac{x}{2} \)
| x > 1\(\frac{1}{2}\) | |
| x > -1\(\frac{7}{41}\) | |
| x > -2\(\frac{2}{3}\) | |
| x > \(\frac{12}{35}\) |
To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the > sign and the answer on the other.
2x + 4 > \( \frac{x}{2} \)
2 x (2x + 4) > x
(2 x 2x) + (2 x 4) > x
4x + 8 > x
4x + 8 - x > 0
4x - x > -8
3x > -8
x > \( \frac{-8}{3} \)
x > -2\(\frac{2}{3}\)