The scale drawing of the rectangular classroom floor has dimensions of 8 inches by 5 inches. The actual length of the longer side of the floor is 32 feet. What is the actual area of the floor in square feet? (2 points) Responses 40 feet2 40 feet2 240 feet2 240 feet2 640 feet2 640 feet2 92,160 feet2 92,160 feet2 Question 2 Show your work for this problem. Be sure to show each step and explain using math vocabulary. (2 points)
First, we need to determine the scale factor used in the drawing. Since the longer side of the floor in the scale drawing is 8 inches and in actuality is 32 feet, we can set up a proportion to find the scale factor:
8 inches / 32 feet = 1/x
Cross multiplying, we get:
8 * x = 32
x = 32 / 8
x = 4
So, the scale factor is 4.
Next, we need to find the actual dimensions of the floor using the scale factor. The shorter side of the floor in the scale drawing is 5 inches, so in actuality it would be:
5 inches * 4 = 20 feet
Therefore, the actual dimensions of the floor are 20 feet by 32 feet.
To find the actual area of the floor, we multiply the actual length by the actual width:
20 feet * 32 feet = 640 feet^2
Therefore, the actual area of the floor is 640 square feet.
can you show me step by step
Sure! Here's a step-by-step explanation:
1. Determine the scale factor:
- We know the longer side of the floor in the scale drawing is 8 inches, and in actuality is 32 feet.
- Set up a proportion: 8 inches / 32 feet = 1/x
- Cross multiply: 8 * x = 32
- Solve for x: x = 32 / 8 = 4
- The scale factor is 4.
2. Find the actual dimensions of the floor:
- The shorter side in the scale drawing is 5 inches.
- Multiply by the scale factor to find the actual shorter side: 5 inches * 4 = 20 feet
- The actual dimensions of the floor are 20 feet by 32 feet.
3. Calculate the actual area of the floor:
- Multiply the actual length by the actual width: 20 feet * 32 feet = 640 square feet
- Therefore, the actual area of the floor is 640 square feet.
bot write it as a 7th grader
Sure! Here's a simpler explanation:
1. Find the scale factor:
- The long side of the floor is 8 inches in the drawing and 32 feet in real life.
- To find the scale factor: 8 inches ÷ 32 feet = 1/x
- Cross multiply: 8 * x = 32
- Solve for x: x = 32 ÷ 8 = 4
- The scale factor is 4.
2. Calculate the actual dimensions of the floor:
- The short side is 5 inches in the drawing.
- To find the actual short side: 5 inches * 4 = 20 feet
- The actual dimensions are 20 feet by 32 feet.
3. Determine the actual area of the floor:
- Multiply the actual length by the width: 20 feet * 32 feet = 640 square feet
- So, the real area of the floor is 640 square feet.