| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.36 |
| Score | 0% | 67% |
If side a = 5, side b = 7, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{10} \) | |
| \( \sqrt{74} \) | |
| \( \sqrt{53} \) | |
| \( \sqrt{82} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 52 + 72
c2 = 25 + 49
c2 = 74
c = \( \sqrt{74} \)
On this circle, line segment CD is the:
radius |
|
chord |
|
diameter |
|
circumference |
A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).
If the area of this square is 1, what is the length of one of the diagonals?
| 7\( \sqrt{2} \) | |
| 2\( \sqrt{2} \) | |
| \( \sqrt{2} \) | |
| 4\( \sqrt{2} \) |
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 = \( \sqrt{a} \) = \( \sqrt{1} \) = 1
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 = 12 + 12
c2 = 2
c = \( \sqrt{2} \)
If side x = 8cm, side y = 11cm, and side z = 5cm what is the perimeter of this triangle?
| 31cm | |
| 22cm | |
| 42cm | |
| 24cm |
The perimeter of a triangle is the sum of the lengths of its sides:
p = x + y + z
p = 8cm + 11cm + 5cm = 24cm
On this circle, line segment AB is the:
chord |
|
diameter |
|
radius |
|
circumference |
A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).