The width of a rectangle is 12 cm less than the length. The perimeter is 156 cm. Find the width and length.
W=L-12
156=2L+2W=2L+2(L-12)
solve for L first,the solve for W
Let's denote the length of the rectangle as L and the width as W.
According to the given information, the width is 12 cm less than the length, so we can write the equation:
W = L - 12
The perimeter of a rectangle can be calculated by the formula:
Perimeter = 2(L + W)
Given that the perimeter is 156 cm, we can substitute the values in the equation:
156 = 2(L + (L - 12))
Simplifying the equation:
156 = 2(2L - 12)
156 = 4L - 24
Adding 24 to both sides:
156 + 24 = 4L
180 = 4L
Now, divide both sides by 4:
180 / 4 = L
L = 45
Substitute the value of L back into the equation for W:
W = L - 12
W = 45 - 12
W = 33
Therefore, the length of the rectangle is 45 cm and the width is 33 cm.
To find the width and length of the rectangle, we can set up a system of equations based on the given information.
Let's assume the length of the rectangle is "L" cm.
According to the problem, the width of the rectangle is 12 cm less than the length, so the width can be represented as: L - 12 cm.
The formula for the perimeter of a rectangle is: P = 2(L + W), where P is the perimeter, L is the length, and W is the width.
Given that the perimeter is 156 cm, we can substitute the values into the equation:
156 = 2(L + (L - 12))
Now, we can solve the equation to find the length of the rectangle (L):
156 = 2(2L - 12)
156 = 4L - 24
4L = 156 + 24
4L = 180
L = 180 / 4
L = 45
So, the length of the rectangle is 45 cm.
To find the width, we substitute the length into the equation for the width:
W = L - 12
W = 45 - 12
W = 33
Therefore, the width of the rectangle is 33 cm and the length is 45 cm.