- If the triangle below is dilated by a scale factor of 2, what is the perimeter of the new triangle?
- 19
- 32
- 44
- 76
Since the original triangle is dilated by a scale factor of 2, the length of each side will be multiplied by 2 to get the side lengths of the new triangle. Therefore, \(8\times2=16\), \(12\times2=24\), and \(18\times2=36\).
Then, \(16+24+36=76\).
- What scale factor was used to scale the rectangle in the figure below?
- \(\frac{1}{4}\)
- \(\frac{1}{3}\)
- 3
- 4
To determine the scale factor, take the side lengths of the scaled rectangle and divide them by the corresponding sides of the original rectangle: \(\frac{1}{4}=\frac{1}{4}\) and \(\frac{3}{12}=\frac{1}{4}\). Therefore, the scale factor used to scale the rectangle is \(\frac{1}{4}\).
- Which of the following sets of angles CANNOT be used to construct a triangle?
- Three acute angles
- Two acute angles and one right angle
- Two acute angles and one obtuse angle
- Two right angles and one acute angle
In order to construct a triangle, the three angles must sum to 180°. In Answer D, the two right angles by themselves would sum to 180°, so adding an acute angle to that value would make the sum greater than 180°. Therefore, a triangle cannot be constructed with two right angles.
- If the right rectangular prism shown below was horizontally sliced, which of the following shapes would BEST describe the resulting two-dimensional shape?
- Parallelogram
- Rectangle
- Rhombus
- Square
Horizontally slicing the right rectangular prism would create slices that are parallel to the base of the prism. Since the base of the prism is a square with sides of length 4, each of the horizontal slices would also be in the shape of a square.
- Kevin is planting vegetables in his garden. If the garden is in the shape of a circle with a diameter of 10 feet, what is the area of the garden?
- 15.7 ft2
- 31.4 ft2
- 78.5 ft2
- 314 ft2
The formula for the area of a circle is \(A= \pi r^2\). Since the diameter of the garden is 10 ft, the radius of the garden is 5 ft. Therefore, \(A=3.14(5 \text{ ft})^2=78.5 \text{ ft} ^2\).
- Tory went to see a monster truck show at the local arena. Before the show, Tory got to see the trucks up close. He noticed that each monster truck tire had a radius of about 3 ft. Based on that radius, what would be the distance around each tire?
- 9.42 ft2
- 18.84 ft2
- 28.32 ft2
- 113 ft2
The distance around each tire is the circumference of the circle:
\(C=2\pi r=2(3.14)(3\text{ ft})=18.84 \text{ ft}\)
- What is the value of \(x\) in the figure below?
- 4
- 6
- 15
- 21
The two angles shown in the figure are supplementary. In order to solve for \(x\), the following equation must be used: \(10x-5+35=180\). This equation simplifies as \(10x+30=180\).
After subtracting 30 from both sides, the equation becomes \(10x=150\). Finally, after dividing both sides by 10, the solution is \(x=15\).
- What is the measure of \(\angle DBC\) in the figure below?
- 10°
- 20°
- 40°
- 50°
Before we can find measure of \(\angle DBC\), we first need to solve for \(x\).
Since \(\angle ABD\) and \(\angle DBC\) are complementary, we need to use the equation \(m \angle ABD + m \angle DBC\) \(= 90\).
Substituting for the values of \(m \angle ABD\) and \(m \angle DBC\), the equation becomes \(5x+4x=90\). This equation simplifies as \(9x=90\).
Finally, after dividing both sides of the equation by 9, the result is \(x=10\). To find the measure of \(\angle DBC\), we substitute \(x=10\) into \((4x)°\) to get \((4 \times 10)°=40°\).
- Jason is building a desk for his bedroom. He wants the desk to fit in the corner of his room and decides to go with a trapezoid design. If Jason uses the dimensions shown in the picture below, how many square feet of plywood will he need to build the desk top?
- 5 ft2
- 6 ft2
- 9 ft2
- 12 ft2
Use the formula for the area of a trapezoid:
\(A = \frac{b_{1} + b_{2}}{2} \times h\)
If we insert our values into the formula, \(b_{1} = 5 \text{ ft}\), \(b_{2} = 1 \text{ ft}\), and \(h = 2 \text{ ft}\).
Therefore, \(A = \frac{5 + 1}{2} \times 2\) \(= 3 \times 2 = 6 \text{ ft}^2\).
- Natalie recently bought a jewelry box, but she wants to re-cover the box with a more colorful fabric. If the jewelry box is a cube with sides 8 cm long, how much fabric will Natalie need in order to cover all sides of the box?
- 64 cm2
- 192 cm2
- 384 cm2
- 512 cm2
The amount of fabric needed to cover the jewelry box is equal to the surface area of the box. The formula for the surface area of a cube is \(SA=6s^2\), where \(s\) is the length of one side. Therefore, the surface area of the jewelry box is as follows:
\(SA=6(8 \text{ cm})^2= 6(64 \text{ cm})^2\) \(=384 \text{ cm}^2\)