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Questions and Answers
Which mathematical operation is necessary to calculate the area of a rectangle?
Which mathematical operation is necessary to calculate the area of a rectangle?
- Addition of lengths
- Multiplication of length and width (correct)
- Subtraction of lengths
- Division of perimeter by 2
What would happen to the area of a rectangle if both the length and width are doubled?
What would happen to the area of a rectangle if both the length and width are doubled?
- The area doubles
- The area increases by four times (correct)
- The area decreases by half
- The area remains the same
In a right triangle, which of the following statements is true about the relationship between the sides?
In a right triangle, which of the following statements is true about the relationship between the sides?
- The hypotenuse is shorter than at least one other side
- The square of the hypotenuse equals the sum of the squares of the other two sides (correct)
- The hypotenuse is equal to the sum of the two other sides
- The length of each side can be any positive number
Which equation represents the distance formula between two points in a coordinate plane?
Which equation represents the distance formula between two points in a coordinate plane?
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What is the volume of a cube with a side length of 3 units?
What is the volume of a cube with a side length of 3 units?
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Study Notes
Area of a Rectangle
- Multiplication is necessary to calculate the area of a rectangle.
- Doubling both the length and width of a rectangle quadruples its area.
Right Triangles
- The Pythagorean theorem applies to right triangles: the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Distance Formula
- The distance formula between two points (x1, y1) and (x2, y2) in a coordinate plane is: √[(x2 - x1)2 + (y2 - y1)2]
Cube Volume
- The volume of a cube is calculated by cubing the length of one side.
- A cube with a side length of 3 units has a volume of 27 cubic units.
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