| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.06 |
| Score | 0% | 61% |
Which of the following is not true about both rectangles and squares?
the perimeter is the sum of the lengths of all four sides |
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the area is length x width |
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the lengths of all sides are equal |
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all interior angles are right angles |
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).
Which of the following statements about a triangle is not true?
exterior angle = sum of two adjacent interior angles |
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perimeter = sum of side lengths |
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area = ½bh |
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sum of interior angles = 180° |
A triangle is a three-sided polygon. It has three interior angles that add up to 180° (a + b + c = 180°). An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite (d = b + c). The perimeter of a triangle is equal to the sum of the lengths of its three sides, the height of a triangle is equal to the length from the base to the opposite vertex (angle) and the area equals one-half triangle base x height: a = ½ base x height.
If the area of this square is 81, what is the length of one of the diagonals?
| 8\( \sqrt{2} \) | |
| 2\( \sqrt{2} \) | |
| \( \sqrt{2} \) | |
| 9\( \sqrt{2} \) |
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 = \( \sqrt{a} \) = \( \sqrt{81} \) = 9
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 = 92 + 92
c2 = 162
c = \( \sqrt{162} \) = \( \sqrt{81 x 2} \) = \( \sqrt{81} \) \( \sqrt{2} \)
c = 9\( \sqrt{2} \)
Simplify (7a)(3ab) - (5a2)(8b).
| 61a2b | |
| 130ab2 | |
| -19a2b | |
| 61ab2 |
To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.
(7a)(3ab) - (5a2)(8b)
(7 x 3)(a x a x b) - (5 x 8)(a2 x b)
(21)(a1+1 x b) - (40)(a2b)
21a2b - 40a2b
-19a2b
If angle a = 70° and angle b = 34° what is the length of angle d?
| 110° | |
| 140° | |
| 137° | |
| 150° |
An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:
d° = b° + c°
To find angle c, remember that the sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 70° - 34° = 76°
So, d° = 34° + 76° = 110°
A shortcut to get this answer is to remember that angles around a line add up to 180°:
a° + d° = 180°
d° = 180° - a°
d° = 180° - 70° = 110°