Q: A triangle has an area of $$30$$ square feet and a base of $$5$$ feet. What is the height of the triangle?

$$h = \frac{2A}{b} = \frac{2 \times 30}{5} = 12$$ feet

Q: A circular swimming pool has a diameter of $$24$$ feet. What is the area of the pool in terms of $$\pi$$?

$$A = \pi r^2$ = \pi (12)^2$ = 144\pi$$ \text{ square feet}$

Q: A cylinder has a radius of $$4 cm $$and a height of $$10 cm. $$What is its volume?

$$V = \pi r^2$ h = \pi (4)^2$ (10) = 160\pi$$ \text{ cm}^3$

Q: A pizza with a diameter of $$16$$ inches costs $$18. $$What is the price per square inch? (Use $$\pi \approx 3.14$$ and round to the nearest cent.)

$$\text{Area} = \pi (8)^2$ = 201.06$$ \text{ in}^2$$, \text{Price per in}^2 = \frac{18}{201.06} \approx 0.09$$

Q: A rectangular solid has length $$l = 5 cm$$, width $$w = 3 cm$$, and height $$h = 2 cm. $$What is its volume?

$$V = lwh = 5 \times 3 \times 2 = 30$$ \text{ cm}^3$

Question 1

A rectangular garden has a length of 12 meters and a width of 7 meters. What is the perimeter of the garden?

Accepted Answer

$$P = 2(12 + 7) = 38$$ meters

Question 2

A triangle has an area of $$30$$ square feet and a base of $$5$$ feet. What is the height of the triangle?

Accepted Answer

$$h = \frac{2A}{b} = \frac{2 	imes 30}{5} = 12$$ feet

Question 3

A circular swimming pool has a diameter of $$24$$ feet. What is the area of the pool in terms of $$\pi$$?

Accepted Answer

$$A = \pi r^2$ = \pi (12)^2$ = 144\pi$$ 	ext{ square feet}$

Question 4

A cone-shaped cup has a radius of $$3 cm $$and a height of $$8 cm. $$What is the volume of the cup?

Accepted Answer

$$V = \frac{1}{3}\pi r^2$ h = \frac{1}{3}\pi (3)^2$ (8) = 24\pi$$ 	ext{ cm}^3$

Question 5

A triangle has angles in the ratio $$2:3:5. $$What are the measures of the three angles?

Accepted Answer

$$36^\circ, 54^\circ, 90^\circ$$

Question 6

If the measure of an angle is $$x$$, what is the measure of its supplement?

Accepted Answer

$$180 - x$$

Question 7

A cylinder has a radius of $$4 cm $$and a height of $$10 cm. $$What is its volume?

Accepted Answer

$$V = \pi r^2$ h = \pi (4)^2$ (10) = 160\pi$$ 	ext{ cm}^3$

Question 8

A pizza with a diameter of $$16$$ inches costs $$18. $$What is the price per square inch? (Use $$\pi \approx 3.14$$ and round to the nearest cent.)

Accepted Answer

$$	ext{Area} = \pi (8)^2$ = 201.06$$ 	ext{ in}^2$$, 	ext{Price per in}^2 = \frac{18}{201.06} \approx 0.09$$

Question 9

A rectangular solid has length $$l = 5 cm$$, width $$w = 3 cm$$, and height $$h = 2 cm. $$What is its volume?

Accepted Answer

$$V = lwh = 5 	imes 3 	imes 2 = 30$$ 	ext{ cm}^3$

Question 10

A sphere has a radius of $$6 cm. $$What is its volume?

Accepted Answer

$$V = \frac{4}{3}\pi r^3$ = \frac{4}{3}\pi (6)^3$ = 288\pi$$ 	ext{ cm}^3$

Question 11

The measure of an angle is three times its supplement. What is the measure of the angle?

Accepted Answer

$$x = 3(180 - x) \implies x = 135^\circ$$

Question 12

A triangle has angles measuring $$x$$, $$2x$$, and $$3x. $$What is the value of $$x$$?

Accepted Answer

$$x + 2x + 3x = 180 \implies 6x = 180 \implies x = 30^\circ$$

Question 13

A rectangular field is $$50$$ meters long and $$20$$ meters wide. What is its area?

Accepted Answer

$$A = l 	imes w = 50 	imes 20 = 1000$$ 	ext{ m}^2$

Question 14

A triangle has angles measuring $$x$$, $$x + 10$$, and $$x + 20. $$What is the value of $$x$$?

Accepted Answer

$$x + (x + 10) + (x + 20) = 180 \implies 3x + 30 = 180 \implies x = 50^\circ$$

Question 15

A rectangular box has a length of $$10 cm$$, width of $$4 cm$$, and height of $$3 cm. If $$the height is doubled, how many times greater is the new volume compared to the original?

Accepted Answer

$$	ext{The new volume is 2$$	imes$$ the original volume}$$

Question 16

If two angles are complementary and one angle is $$x$$, what is the measure of the other angle?

Accepted Answer

$$90 - x$$

Question 17

A trapezoid has bases of $$8 cm $$and $$12 cm$$, and a height of $$5 cm. $$What is its area?

Accepted Answer

$$A = \frac{1}{2}(b_1$ + b_2$)h = \frac{1}{2}(8 + 12)5 = 50$$ 	ext{ cm}^2$

Linear Equations and Inequalities in One Variable: Applications in Geometry

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