The perimeter of a rectangle is 122 feet and the length is 10 times longer than twice the width. Find the dimension.
L = 10(2W) = 20W
122 = 2L + 2W
Substitute 20W for L
122 = 2(20W) + 2W = 42W
Divide both sides by 42 to find W, then calculate L.
To solve this problem, we need to set up equations based on the given information.
Let's assume that the width of the rectangle is "w" feet.
According to the given information, the length of the rectangle is 10 times longer than twice the width. So, the length can be represented as 2w * 10 = 20w.
The perimeter of a rectangle can be calculated by adding the lengths of all four sides. In this case, it can be represented as:
Perimeter = 2(length + width)
So, we have the equation 122 = 2(20w + w).
Now, let's solve the equation step by step to find the value of "w", which represents the width of the rectangle.
First, simplify the equation:
122 = 2(21w)
122 = 42w
Next, divide both sides of the equation by 42 to isolate "w":
w = 122/42
w = 61/21
So, the width of the rectangle is 61/21 feet.
To find the length, substitute the value of "w" into the expression for the length:
Length = 20w
Length = 20 * (61/21)
Length = 1220/21
Therefore, the dimensions of the rectangle are approximately:
Width = 61/21 feet
Length = 1220/21 feet