A rectangle is 7 times as long as it is wide. The perimeter is 80 feet. find the dimensions.
How did you do this? What are the steps? I would like to know how to figure this out too. Thank you.
P = 2L + 2W
80 = 2(7W) + 2W
80 = 16W
5 = W
Let's assume the width of the rectangle is "w" feet.
According to the given information, the length of the rectangle is 7 times the width, which means the length is 7w feet.
The perimeter of a rectangle is given by the formula: perimeter = 2 * (length + width)
Substituting the values, we can write the equation as:
80 = 2 * (7w + w)
To simplify further, we combine the like terms inside the brackets:
80 = 2 * 8w
Dividing both sides of the equation by 2:
40 = 8w
Next, divide both sides of the equation by 8:
5 = w
So, the width of the rectangle is 5 feet.
To find the length, we substitute this value back into the expression 7w:
length = 7w = 7 * 5 = 35 feet
Therefore, the dimensions of the rectangle are: width = 5 feet and length = 35 feet.
To find the dimensions of the rectangle, we can set up two equations based on the given information.
Let's assume the width of the rectangle is represented by 'w', and the length of the rectangle is represented by 'l'.
1. We are told that the rectangle is 7 times as long as it is wide, so we can write the equation:
l = 7w
2. The perimeter of a rectangle is given by the formula:
Perimeter = 2(l + w)
We are also told that the perimeter of the rectangle is 80 feet, so we can write the equation:
80 = 2(l + w)
Now, we can solve these two equations simultaneously to find the values of 'w' and 'l'.
Substitute the value of 'l' from equation 1 into equation 2:
80 = 2(7w + w)
Simplify the equation:
80 = 2(8w)
80 = 16w
Divide both sides of the equation by 16:
w = 5
Now substitute the value of 'w' back into equation 1 to find 'l':
l = 7w
l = 7(5)
l = 35
Therefore, the dimensions of the rectangle are:
Width = 5 feet
Length = 35 feet