37,607 views
26 votes
26 votes
2. The area of the arena is 2160 in.2 a) Will the arena fit on the rug? Show your work and explain your answer below. b) If the length of the arena is 60 inches, what is the width? c) If the arena fits, and is placed exactly in the middle of the rug, how much standing room on the rug could a drive have? Use your measurements from above to help you. ? 3. If 15 robots can fit on the arena floor at one time, how much space does each robot take up?

2. The area of the arena is 2160 in.2 a) Will the arena fit on the rug? Show your-example-1
User JohnGoldsmith
by
2.8k points

1 Answer

25 votes
25 votes

Answers:

2a. The arena will fit on the rug

b. Width = 36 in

c. Standing room: 4 in

3. 144 in²

Step-by-step explanation:

2. Part a.

First, we need to convert the measures of the rug to inches, so taking into account that 1 ft = 12 in, we get

Length = 6 ft x 12 in/ 1ft = 72 in

Width = 4 ft x 12 in/ 1 ft = 48 in

Then, the area of the rug will be

Area = Length x Width

Area = 72 in x 48 in

Area = 3456 in²

Therefore, the area of the arena, which is 2160 in² is lower than the area of the rug. It means that the area will fit on the rug.

Part b.

The area of the arena is equal to

Area = Length x Width

To find the width of the area, we need to solve the equation for the width, so

Width = Area/Length

So, replacing Area = 2160 in² and Length = 60 in, we get

Width = 2160 in² / 60 in

Width = 36 in

Therefore, the width of the area is 36 in.

Part c.

The measures that we get from parts a and b can be represented as

Therefore, the missing length can be calculated as:

(48 in - 36 in)/2 = 12 in/ 2 = 6 in

Therefore, a drive will have 6 in of standing room.

3.

Finally, to know how much space each robot take up, we need to divide the area of the arena by 15, so

2160 in²/ 15 = 144 in²

Therefore, each robot take 144 in²

2. The area of the arena is 2160 in.2 a) Will the arena fit on the rug? Show your-example-1
User Mathiasfk
by
2.7k points