A composite shape is drawn, starting with a horizontally aligned rectangle. There is no measurement across the top, and the right side is labeled with a question mark. A horizontally aligned rectangular area marked as 8 feet in length and unknown in width is removed from the bottom left of the original rectangle. The remaining length on the bottom of the right side is 2 feet. The remaining width on the left side is 3 feet. All the corners are marked with right angles.
Tessa designs a supply closet as an addition to her house. The closet is pictured, and its total area is 36 square feet. What is the length in feet of the side of the supply closet labeled with the question mark? (1 point)
To find the length of the side labeled with the question mark, we need to subtract the area of the removed rectangular area from the total area of the shape.
Total area = 36 square feet
Area of removed rectangular area = 8 feet x unknown width = 8w
Remaining area = Total area - Area of removed rectangular area
Remaining area = 36 sq ft - 8w sq ft
Since the remaining length on the bottom of the right side is 2 feet and the remaining width on the left side is 3 feet, the remaining rectangular area is 3 feet x 2 feet = 6 square feet.
Equating the remaining area to 6 sq ft:
36 sq ft - 8w sq ft = 6 sq ft
8w = 30
w = 30/8
w = 3.75 feet
Therefore, the width of the side labeled with the question mark is 3.75 feet.
How did you get that answer?
I apologize for the mistake in my previous response. Let's calculate the correct answer.
Given:
Total area = 36 square feet
Length of removed rectangular area = 8 feet
Width of removed rectangular area = unknown (let's call it x)
Remaining area = Total area - Area of removed rectangular area
Remaining area = 36 sq ft - 8 ft * x ft
Since the remaining length on the bottom of the right side is 2 feet and the remaining width on the left side is 3 feet, the remaining rectangular area is 3 feet x 2 feet = 6 square feet.
So,
Remaining area = 6 square feet
We can set up the equation as follows:
36 - 8x = 6
Solving for x:
36 - 6 = 8x
30 = 8x
x = 30/8
x = 3.75 feet
Therefore, the width of the side labeled with the question mark is 3.75 feet.
can you explain how you got that answer?
Of course! Let's break it down step by step.
1. Given information:
- Total area of the shape = 36 square feet
- Length of the removed rectangular area = 8 feet
- The width of the removed rectangular area is unknown, so we will denote it as x.
2. Calculating the remaining area:
The remaining area after removing the 8 feet length rectangular area is 36 sq ft - (8 ft * x ft).
This is because, after removing the 8 feet by x feet rectangular area, the total area of the remaining shape is 36 sq ft.
3. We know that the remaining rectangular area (which is rectangular in shape with remaining length and width) is 2 feet by 3 feet, giving an area of 6 square feet.
4. Setting up the equation:
Given that the remaining area is 6 sq ft, we can set up the equation:
36 - 8x = 6
5. Solving for x:
36 - 8x = 6
Subtracting 36 from both sides:
-8x = 6 - 36
-8x = -30
Dividing by -8 on both sides:
x = -30 / -8
x = 3.75 feet
Therefore, the correct answer is that the width of the side labeled with the question mark is 3.75 feet. Thank you for your patience!
so 3 x 8 = 24, so 36 - 24 = 12. 12 / 2 = 6, so the missing amount is six
Thank you for your calculation. Let's double-check to ensure correctness.
Given:
Total area = 36 square feet
Length of the removed rectangular area = 8 feet
Calculating the remaining area:
36 sq ft - 8 ft * x ft = Remaining area
Using your calculation:
36 - 8 * 3 = 12 square feet
This implies that the remaining area after removing the 8 feet by 3 feet rectangular area is 12 square feet.
However, based on the information provided, we know that the remaining rectangular area on the right side is 2 feet in length and the remaining width on the left side is 3 feet, which gives an area of 6 square feet, not 12 square feet.
Therefore, the correct calculation would be:
36 sq ft - (8 ft * 3 ft) = 36 sq ft - 24 sq ft = 12 sq ft
12 sq ft / 2 = 6
Thus, the missing amount is 6 square feet, and the width of the side labeled with the question mark is 6 feet. Thank you for your contribution.