a rectangle's width is one-seventh its length, its perimeter is 160m. find the dimensions of the rectangle.
P = 2L + 2W
160 = (2 * 7W) + 2W
160 = 16W
10 = W
To find the dimensions of the rectangle, we need to set up an equation using the given information.
Let's assume that the length of the rectangle is "L" and the width of the rectangle is "W." According to the problem, the width (W) is one-seventh (1/7) of its length (L).
Mathematically, we can express this relationship as:
W = (1/7)L
Now, we also know that the perimeter of a rectangle is calculated by adding the lengths of all four sides together. In this case, the perimeter is given as 160 meters. The formula for the perimeter (P) of a rectangle is:
P = 2L + 2W
Substituting the value of W from the first equation into the second equation, we get:
160 = 2L + 2(1/7)L
Simplifying this equation, we get:
160 = 2L + (2/7)L
To solve this equation, we can multiply both sides by 7 to eliminate the fraction:
160 * 7 = 14L + 2L
1120 = 16L
Next, divide both sides of the equation by 16 to solve for L:
L = 1120 / 16
L = 70
So, the length of the rectangle is 70 meters.
To find the width, we can substitute the value of L back into the first equation:
W = (1/7) * 70
W = 10
Therefore, the dimensions of the rectangle are length = 70 meters and width = 10 meters.