Use the image to answer the question.
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 right side is 2 feet. The remaining width on the left side is 3 feet. 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?
To find the length of the side labeled with the question mark, we first need to calculate the total area of the composite shape.
The original rectangle has a width of 3 feet and a length of X feet (labeled with a question mark).
The rectangular area removed from the bottom left has a width of 8 feet and a length of X feet.
The total area can be calculated as:
Total Area = (3 + X)(X) - 8(8)
Given that the total area is 36 square feet:
36 = (3 + X)(X) - 64
36 = 3X + X^2 - 64
X^2 + 3X - 100 = 0
Now we can solve for X using the quadratic formula:
X = (-3 ± sqrt(3^2 - 4*1*(-100))) / 2*1
X = (-3 ± sqrt(9 + 400)) / 2
X = (-3 ± sqrt(409)) / 2
X = (-3 ± 20.22) / 2
Since the length cannot be negative, we take the positive value:
X = (20.22 - 3) / 2
X = 17.22 / 2
X ≈ 8.61 feet
Therefore, the length of the side labeled with the question mark is approximately 8.61 feet.
awnser i got was 6
I apologize for the error in my previous calculation. Let's calculate the correct answer.
We had the equation:
X^2 + 3X - 100 = 0
Using the quadratic formula:
X = (-3 ± sqrt(3^2 - 4*1*(-100))) / 2*1
X = (-3 ± sqrt(9 + 400)) / 2
X = (-3 ± sqrt(409)) / 2
Since we are looking for the positive value of X:
X = (-3 + √409) / 2
X = (-3 + 20.22) / 2
X = 17.22 / 2
X ≈ 8.61 feet
Therefore, the correct length of the side labeled with the question mark is approximately 8.61 feet. Thank you for pointing out the mistake.
no, because i cut the form into two. the larger form was 30, so the smaller one was six, as the lower half of the line was 3 and 3 x 2 = 6, so add 6 to 30 and we get thirt six
Thank you for providing additional clarification. In that case, we can approach the calculation as follows:
The total area of the composite shape is 36 square feet.
The original rectangle has a width of 3 feet and a length of X feet.
The rectangular area removed from the bottom left has a width of 8 feet and a length of X feet.
So, the area of the original rectangle is:
Original rectangle area = 3 * X = 3X
The area removed is:
Area removed = 8 * 6 = 48
As per your explanation, the remaining rectangle has an area of 30 square feet:
Total area = Original rectangle area - Area removed = 3X - 48 = 30
3X - 48 = 30
3X = 30 + 48
3X = 78
X = 78 / 3
X = 26
Therefore, the length of the side labeled with the question mark (X) is 26 feet. Thank you for providing the additional details to arrive at the correct answer.