The ratio of the length of a rectangle to the width is 7:2. If the total distance around the rectangle is 54 feet, what the length and with of the rectangle?
L = (7/2)w
2w+2L = 54
w+L = 27
w + (7/2) w = 27
2 w + 7 w = 27*2
9 w = 27 * 2
w = 3 * 2
To find the length and width of the rectangle, we can use the given ratio and the total distance around the rectangle.
Let's assume that the length of the rectangle is 7x feet and the width is 2x feet, where x is a common factor.
The total distance around the rectangle is given as 54 feet, which is the perimeter.
The formula for the perimeter of a rectangle is: Perimeter = 2 * (Length + Width)
Substituting the values, we can write the equation as:
54 = 2 * (7x + 2x)
Simplifying the equation, we get:
54 = 2 * 9x
54 = 18x
Dividing both sides of the equation by 18, we find:
x = 3
Now, we can substitute the value of x back into the expression for the length and width of the rectangle:
Length = 7x = 7 * 3 = 21 feet
Width = 2x = 2 * 3 = 6 feet
Therefore, the length of the rectangle is 21 feet and the width is 6 feet.
To solve this problem, we can set up a system of equations. Let's say the length of the rectangle is represented by 7x, and the width is represented by 2x.
We know that the total distance around a rectangle, also known as the perimeter, is equal to the sum of all its sides. In this case, the perimeter is given as 54 feet.
The formula for the perimeter of a rectangle is P = 2(L + W), where P represents the perimeter, L represents the length, and W represents the width.
Plugging in the values, we can write the equation as 54 = 2(7x + 2x).
Simplifying this equation, we get 54 = 2(9x), which further simplifies to 54 = 18x.
Dividing both sides of the equation by 18, we find x = 3.
Now that we have the value of x, we can substitute it back into the expressions for the length and width.
Length = 7x = 7(3) = 21 feet.
Width = 2x = 2(3) = 6 feet.
Therefore, the length of the rectangle is 21 feet, and the width is 6 feet.