A rectangular Persian carpet has a perimeter of 212 inches. The length of the carpet is 24 inches more than the width. What are the dimensions of the carpet?
P = 2L + 2W
212 = 2(W + 24) + 2W
212 = 4W + 48
164 = 4W
41 = W
Thank you for helping Ms. Sue.
The width of an oriental carpet is 2 ft less than the length. The perimeter of the carpet is 24 ft. Find the dimensions of the carpet.
Well, aren't you fancy with your Persian carpet question! Now, let's solve it. Let's call the width of the carpet "W", because why not? Now, we know that the length is 24 inches more than the width, so the length would be "W + 24".
Now, let's talk about the perimeter. The formula for finding the perimeter of a rectangle is 2 times the length plus 2 times the width. So, using this formula, we can say:
2(W + 24) + 2W = 212
Simplifying this equation, we get:
2W + 48 + 2W = 212
Combining like terms, we get:
4W + 48 = 212
Now, let's subtract 48 from both sides:
4W = 164
Finally, dividing both sides by 4, we can determine the width:
W = 41
So, the width of the carpet is 41 inches. Since the length is 24 inches more than the width, we can calculate:
W + 24 = 41 + 24 = 65
Therefore, the dimensions of the carpet are 41 inches by 65 inches. Enjoy your fancy Persian carpet!
To find the dimensions of the rectangular Persian carpet, we can set up a system of equations based on the given information.
Let's assume the width of the carpet is x inches.
According to the problem, the length of the carpet is 24 inches more than the width, so the length would be (x + 24) inches.
The perimeter of a rectangle is given by the formula: P = 2(length + width).
In this case, the perimeter of the carpet is given as 212 inches. So, we can write the equation as:
212 = 2[(x + 24) + x]
Now, we can simplify the equation and solve for x:
212 = 2(2x + 24)
212 = 4x + 48
4x = 212 - 48
4x = 164
x = 164/4
x = 41
Therefore, the width of the carpet is 41 inches.
To find the length of the carpet, we can substitute the value of x back into the equation:
Length = x + 24 = 41 + 24 = 65
So, the dimensions of the rectangular Persian carpet are 41 inches (width) by 65 inches (length).