The length of Karen's living room is 2ft longer than the width. The perimeter is 80ft. Find the length and the width.
Can someone please explain to me how you find the answers? Thanks a ton!
L = W + 2
P = 2L + 2W
80 = 2(W + 2) + 2W
80 = 2W + 4 + 2W
80 = 4W + 4
76 = 4W
19 = W
Well, well, well, it seems Karen's living room is giving us a little geometry challenge! Don't worry, I'm here to help with a touch of humor.
Let's call the width of Karen's living room "W" (because "Narrow" would be rude) and the length "L" (for "Loong").
Now, according to our problem, L equals 2 feet plus the width, which gives us L = W + 2. Remember that equation, it'll come in handy!
Moving on to the perimeter, my dear friend. By definition, the perimeter is the sum of all sides of a shape. For a rectangle, it can be calculated as P = 2L + 2W.
In this case, our perimeter is 80 feet, so we can set up the following equation: 80 = 2L + 2W.
Now, let's plug in the value of L in terms of W into the equation. Remember that sneaky equation from earlier? L = W + 2. So we have 80 = 2(W + 2) + 2W.
Simplifying that a bit will give us 80 = 2W + 4 + 2W. Combining like terms, we get 80 = 4W + 4.
To make things easier, let's move that 4 to the other side of the equation. Subtracting 4 from both sides, we have 76 = 4W.
And finally, let's divide both sides by 4 to find the value of W. Drumroll, please... W = 19.
Oh, and since L = W + 2, L = 19 + 2, which gives us L = 21.
So, Karen's living room has a width of 19 feet and a length of 21 feet. Voila! Problem solved, with a dash of clowny humor.
To find the length and width of Karen's living room, we can set up equations based on the given information and solve them simultaneously.
Let's assume the width of the living room is x ft.
According to the problem, the length of the living room is 2 ft longer than the width, so it would be (x + 2) ft.
The perimeter of a rectangular shape is the sum of all its sides. In this case, it is given to be 80 ft. So, we can set up the equation:
Perimeter = 2*(Length + Width)
Substituting the values we have:
80 = 2*((x + 2) + x)
Now, we can solve this equation for x:
80 = 2*(2x + 2)
80 = 4x + 4
76 = 4x
x = 19
So, the width of the living room is 19 ft.
To find the length, we substitute this value of x back into the equation for the length:
Length = x + 2
Length = 19 + 2
Length = 21
Therefore, the length of Karen's living room is 21 ft.
In summary, the width is 19 ft and the length is 21 ft.
To find the length and width of Karen's living room, we can use the information given in the problem. Let's break it down step by step:
1. Let's assume the width of the living room is "x" feet. Since the length is 2 feet longer than the width, we can say the length is (x + 2) feet.
2. The perimeter of a rectangle is the sum of all four sides. In this case, it is given as 80 feet. The formula for the perimeter is P = 2(L + W).
We can substitute the length and width values into the equation:
80 = 2(x + 2 + x)
3. Simplify the equation:
80 = 2(2x + 2)
Divide both sides of the equation by 2:
40 = 2x + 2
4. Subtract 2 from both sides of the equation:
40 - 2 = 2x
38 = 2x
5. Divide both sides of the equation by 2:
38/2 = x
x = 19
6. Now that we know the width (x = 19), we can find the length by substituting it into the equation:
length = x + 2 = 19 + 2 = 21
Therefore, the width of Karen's living room is 19 feet, and the length is 21 feet.