The width of a rectangle is 12cm less than the length the perimeter is 156cm find the width and length
Width = w
Length L = w + 12
Perimeter = 2L + 2w = 2w + 24 + 2w = 156
4w = 156 -24 = 132
Can you solve that?
Let's denote the length of the rectangle as "L" and the width as "W".
According to the given information, we can set up two equations:
1) The width is 12cm less than the length: W = L - 12
2) The perimeter of a rectangle is calculated as 2 times the sum of the length and width: 2(L + W) = 156
Now we can solve these equations step-by-step to find the values of L and W.
Step 1: Substitute the value of W from equation 1 into equation 2:
2(L + L - 12) = 156
Step 2: Simplify the equation:
2(2L - 12) = 156
4L - 24 = 156
Step 3: Rearrange the equation:
4L = 156 + 24
4L = 180
Step 4: Divide both sides of the equation by 4 to solve for L:
L = 180/4
L = 45
Step 5: Substitute the value of L back into equation 1 to find W:
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 a rectangle, we can set up an equation based on the given information and solve for the variables.
Let's assume the length of the rectangle is "x" cm. According to the given information, the width is 12 cm less than the length, so the width can be expressed as (x - 12) cm.
The perimeter of a rectangle can be calculated by adding the lengths of all four sides. For a rectangle, the perimeter is given as:
Perimeter = 2(length + width)
Substituting the values from our assumptions, we can write the equation:
156 = 2(x + (x - 12))
Now, let's solve this equation to find the values of "x" and then determine the width and length.
Step 1: Distribute the 2 to the terms inside the parentheses:
156 = 2(2x - 12)
Step 2: Simplify the equation:
156 = 4x - 24
Step 3: Move the constant term to the other side of the equation:
156 + 24 = 4x
180 = 4x
Step 4: Divide both sides of the equation by 4:
x = 180/4
x = 45
So, the length of the rectangle is 45 cm.
Now let's find the width by substituting this value back into our expression of width:
Width = x - 12 = 45 - 12 = 33 cm.
Therefore, the width of the rectangle is 33 cm and the length is 45 cm.