A rectangular Persian carpet has a perimeter of 216 inches. The length of the carpet is 30 inches more than the width. What is the dimension of the carpet
w + L = 108
L = w + 30
so
w + w + 30 = 108
Let's assign a variable to the width of the carpet.
Let x be the width of the carpet.
According to the information given, the length of the carpet is 30 inches more than the width, so the length is x + 30.
The perimeter of a rectangle is given by the formula P = 2(length + width).
In this case, the perimeter is 216 inches, so we can set up the equation:
216 = 2(x + (x + 30))
Now we can solve for x:
216 = 2(2x + 30)
Simplify:
216 = 4x + 60
Subtract 60 from both sides:
156 = 4x
Divide both sides by 4:
39 = x
So the width of the carpet is 39 inches.
The length is 30 inches more than the width:
Length = x + 30 = 39 + 30 = 69 inches.
Therefore, the dimensions of the carpet are 39 inches (width) and 69 inches (length).
To solve this problem, let's denote the width of the carpet as "W" inches and the length as "L" inches.
Given that the perimeter of the carpet is 216 inches, we can write the equation for the perimeter as:
Perimeter = 2(length + width)
Substituting the given information into the equation, we have:
216 = 2(L + W)
Since we also know that the length of the carpet is 30 inches more than the width, we can write the equation L = W + 30.
Now we can substitute the value of L in terms of W into the perimeter equation:
216 = 2((W + 30) + W)
Simplifying the equation:
216 = 2(2W + 30)
216 = 4W + 60
156 = 4W
W = 39
Now we can substitute the value of W back into the equation L = W + 30 to find L:
L = 39 + 30
L = 69
Therefore, the width of the carpet is 39 inches and the length is 69 inches.