A rectangular Persian carpet has a perimeter of 240 inches. The length of the carpet is 30 inches more than the width. What are the dimensions of the carpet? Use P = 2L + 2W.
a square carpet has a perimeter of36 ft.find the length of each side of the carpet
To find the dimensions of the rectangular Persian carpet, we need to set up and solve a system of equations based on the given information.
Let's start by assigning variables to the unknowns. Let's call the width of the carpet "W" and the length of the carpet "L".
According to the problem, the length of the carpet is 30 inches more than the width. Thus, we have the equation: L = W + 30.
The formula for the perimeter of a rectangle is P = 2L + 2W. We are given that the perimeter of the carpet is 240 inches. Therefore, we can write the equation as: 240 = 2L + 2W.
Now, we can substitute the expression for L into the perimeter equation:
240 = 2(W + 30) + 2W.
Let's simplify the equation:
240 = 2W + 60 + 2W.
240 = 4W + 60.
Next, let's isolate the variable by subtracting 60 from both sides:
240 - 60 = 4W.
180 = 4W.
To find the value of W, we divide both sides of the equation by 4:
180/4 = W.
45 = W.
Therefore, the width of the carpet is 45 inches.
To find the length of the carpet, we can substitute the value of W back into the equation L = W + 30:
L = 45 + 30.
L = 75.
Thus, the dimensions of the carpet are a width of 45 inches and a length of 75 inches.
L = 30 + W
P = 2L + 2W
240 = 2(30 + W) + 2W
240 = 60 + 2W + 2W
240 - 60 = 60 - 60 + 4W
180 = 4W
45 = W