The perimeter of a rectangular wall is 56m, there are 4 circular windows with a circumference of 7,54m each, the wall has 2 standard doors. What is the length and the width of the wall?
To find the length and width of the rectangular wall, we can set up an equation based on the given information.
Let's assume the length of the wall is L and the width of the wall is W.
The perimeter of a rectangle is given by the formula: P = 2L + 2W
In this case, we are given that the perimeter is 56m, so we can write the equation as:
56 = 2L + 2W ---(Equation 1)
Since the wall has 2 standard doors and 4 circular windows, we can subtract their circumferences from the perimeter of the wall.
Each standard door contributes to the perimeter by its width, and each circular window contributes by its circumference.
Given that the circumference of each circular window is 7.54m, the total contribution of the windows to the perimeter is 4 * 7.54 = 30.16m.
Given that each standard door has a width, the total contribution of the doors to the perimeter is 2 * W.
Since we know the total contribution of the windows and doors to the perimeter, we can now rewrite Equation 1 as:
56 = 2L + 2W - 30.16 - 2W
Simplifying the equation, we get:
56 = 2L - 30.16
Adding 30.16 to both sides of the equation, we get:
56 + 30.16 = 2L
86.16 = 2L
Dividing both sides of the equation by 2, we get:
L = 86.16 / 2
L = 43.08m
So, the length of the wall is 43.08m.
Now, we can substitute this value of L in Equation 1 to find the width.
56 = 2(43.08) + 2W
56 = 86.16 + 2W
Subtracting 86.16 from both sides of the equation, we get:
56 - 86.16 = 2W
-30.16 = 2W
Dividing both sides of the equation by 2, we get:
W = -30.16 / 2
W = -15.08m
Since the width cannot be negative, we can conclude that there is an error in the given information or calculation. Please recheck the values provided.