The perimeter of a rectangle is
192 feet. The length of the rectangle is twice the width. Find the length and width of the rectangle.
It would have been easier to do this than to type it out.
L = 2 w
and
2 L + 2 w = 192
so
2 (2w) + 2 w = 192
3 w = 96
etc
Why did the rectangle go to the doctor? Because it was feeling a little "ill-rect-angle"!
But let's get to the math!
Let's say the width of the rectangle is "w" feet. Since the length is twice the width, we can say the length is "2w" feet.
The formula for the perimeter of a rectangle is given by:
Perimeter = 2(Length + Width)
Given that the perimeter is 192 feet, we can set up the equation as follows:
192 = 2(2w + w)
Simplifying the equation, we get:
192 = 2(3w)
Dividing both sides by 2, we have:
96 = 3w
Now, divide both sides by 3:
w = 32
So, the width of the rectangle is 32 feet.
Since the length is twice the width, the length is:
2w = 2(32) = 64
Therefore, the length of the rectangle is 64 feet and the width is 32 feet. Ta-da!
Let's represent the width of the rectangle as x.
Given that the length of the rectangle is twice the width, we can express the length as 2x.
The formula for the perimeter of a rectangle is: P = 2(length + width).
Substituting the values we have, the equation becomes: 192 = 2(2x + x).
Simplifying the equation: 192 = 2(3x).
Next, we can remove the parentheses by distributing the 2: 192 = 6x.
To isolate x, divide both sides of the equation by 6: x = 192/6.
Simplifying further: x = 32.
So, the width of the rectangle is 32 feet.
Since the length is twice the width, the length is: 2 * 32 = 64 feet.
Therefore, the length and width of the rectangle are 64 feet and 32 feet, respectively.
To solve this problem, let's assign variables to the length and width of the rectangle. Let's say that the width is "w" feet.
According to the problem, the length of the rectangle is twice the width. Therefore, the length is "2w" feet.
The perimeter of a rectangle is found by adding up all the sides, so we can calculate it using the formula:
Perimeter = 2(Length + Width)
Substituting the values we found into the formula:
192 = 2(2w + w)
Simplifying inside the brackets:
192 = 2(3w)
Distributing the 2:
192 = 6w
Now, we can solve for "w" by dividing both sides of the equation by 6:
w = 192 / 6
w = 32
Therefore, the width of the rectangle is 32 feet.
To find the length, we substitute the value of "w" back into our equation:
Length = 2w
Length = 2 * 32
Length = 64
Hence, the length of the rectangle is 64 feet.