the length of a rectangle is 7 feet more than the width. If the perimeter is 194 feet, what are the length and the width?
P = 2L + 2W
194 = 2(7 + W) + 2W
194 = 14 + 4W
180 = 4W
45 = W
Ah, the wondrous world of rectangles! Now, let's tackle this situation like I tackle a clown car - with a dash of humor and some math magic.
Let's call the width of the rectangle "W" (because "Sir Width" wouldn't appreciate being called anything else). According to the problem, the length of the rectangle is 7 feet more than the width. So, the length would be "W + 7" (because it has a fancy little addition going on there).
Now, let's dance into the world of perimeters. The perimeter of a rectangle is calculated by adding up all the side lengths. In this case, we have two lengths and two widths. So, we can write an equation that says:
2(W + (W + 7)) = 194
Now, it's time to unravel this mathematical riddle. Let me plug in my numbers and see what we get. Give me a second; I'm quite the jokester, but math does need a bit of concentration.
2(2W + 7) = 194
Alright! It's time to make this equation squeak like a rubber duck. Let's do some distribution:
4W + 14 = 194
Now, let's get rid of that "funny little 14" by subtracting it from both sides:
4W = 180
And finally, let's find the width W by dividing both sides by 4:
W = 45
So, the width of our rectangle is 45 feet. But wait, there's more! Since the length is 7 feet more than the width, we find that the length is:
W + 7 = 45 + 7 = 52
Voila! So, our rectangle has a length of 52 feet and a width of 45 feet. Don't let it fool you with its fancy angles and symmetric sides!
Let's denote the width of the rectangle as "w". According to the problem, the length of the rectangle is 7 feet more than the width, which means the length can be represented as "w + 7".
To find the perimeter of a rectangle, we add up the lengths of all four sides. Since a rectangle has two pairs of equal sides, we can use the formula:
Perimeter = 2(length + width)
Given that the perimeter is 194 feet, we can set up the equation:
194 = 2(w + w + 7)
Simplifying this equation:
194 = 2(2w + 7)
194 = 4w + 14
Subtracting 14 from both sides:
194 - 14 = 4w
180 = 4w
Dividing both sides by 4:
180/4 = w
45 = w
Therefore, the width of the rectangle is 45 feet.
To find the length, we can substitute the value of w back into our earlier expression:
Length = w + 7 = 45 + 7 = 52 feet
So, the length of the rectangle is 52 feet and the width is 45 feet.
To find the length and width of the rectangle, we can set up equations based on the information given.
Let's assume the width of the rectangle is "x" feet.
According to the given information, the length of the rectangle is 7 feet more than the width. So the length would be "x + 7" feet.
The perimeter of a rectangle is calculated by adding the lengths of all four sides. The formula for the perimeter of a rectangle is:
Perimeter = 2(length + width)
In this case, we are given that the perimeter is 194 feet.
So we can set up the equation:
194 = 2(x + x + 7)
Now let's solve for x:
194 = 2(2x + 7) [Combine like terms]
194 = 4x + 14 [Distribute the 2]
194 - 14 = 4x [Subtract 14 from both sides]
180 = 4x [Simplify]
To find the value of x, divide both sides of the equation by 4:
180/4 = x
45 = x
Therefore, the width of the rectangle is 45 feet.
Now, we can find the length by adding 7 to the width:
Length = x + 7 = 45 + 7 = 52 feet
So, the length of the rectangle is 52 feet, and the width is 45 feet.