The length of a rectangle is 2cm less than 7 times the width the perimeter is 60cm find the width and length
width--- x
length --- 7x-2
solve for x ...
2x + 2(7x-2) = 60
To find the width and length of the rectangle given the perimeter, we can solve a system of equations.
Let's assume that the width of the rectangle is represented by "w" cm and the length is represented by "l" cm.
According to the given information, we can form two equations:
1. The length of the rectangle is 2 cm less than 7 times the width:
l = 7w - 2 ---(Equation 1)
2. The perimeter of a rectangle is the sum of all its sides, which can be calculated using the formula:
perimeter = 2(l + w) = 60
Now, we need to substitute Equation 1 into Equation 2 to eliminate the variable "l":
2((7w - 2) + w) = 60
2(8w - 2) = 60
16w - 4 = 60
16w = 64
w = 4
Now, we have found the width of the rectangle, which is 4 cm.
To find the length, we can substitute the value of "w" (4) into Equation 1:
l = 7w - 2
l = 7(4) - 2
l = 28 - 2
l = 26
Therefore, the length of the rectangle is 26 cm.
In summary, the width of the rectangle is 4 cm, and the length is 26 cm.