a student is painting one wall of a room. a square window is located in the middle of the wall to be painted. the window measures 3 feet on one side. the area of the wall, not including the window, is 80ft squared. find the height of the wall to the nearest tenth.
area of whole wall = 80+9 = 89 ft^2
area = bh , where b is the base and h is the height
h = 89/b
you are missing information.
4square root.Of 5
To find the height of the wall, we need to determine the area of the wall that is not occupied by the window.
1. Calculate the area of the window: Since the window is square, we can find its area by squaring the length of one side.
Area of the window = (side length)^2 = 3^2 = 9 ft^2.
2. Subtract the area of the window from the total area of the wall to find the remaining area that needs to be painted.
Remaining area = Total area - Area of the window = 80 ft^2 - 9 ft^2 = 71 ft^2.
3. The remaining area represents the area of a rectangle, which can be calculated by multiplying the height (h) of the wall by its length (L):
Area of the rectangle = height * length = h * L.
4. Rearrange the equation to solve for the height:
height = remaining area / length = 71 ft^2 / L.
Since we don't have the length of the wall, we cannot calculate the exact height.
To find the height of the wall, we need to determine the area of the wall excluding the window and then use that information to calculate the height.
First, let's find the area of the window by squaring its side length:
Area of the window = side length × side length
Area of the window = 3 ft × 3 ft
Area of the window = 9 ft²
Now, we can subtract the area of the window from the total area of the wall to find the area of the painted portion:
Area of the painted portion = Total area of the wall - Area of the window
Area of the painted portion = 80 ft² - 9 ft²
Area of the painted portion = 71 ft²
Since the painted portion is a square, we can find the length of one side by taking the square root of the area:
Side length of the painted portion = √(Area of the painted portion)
Side length of the painted portion = √(71 ft²)
Side length of the painted portion ≈ 8.4 ft
Since the height of the wall is the same as the side length of the painted portion, the height of the wall is approximately 8.4 ft to the nearest tenth. Therefore, the height of the wall is 8.4 ft.