the perimeter of a rectangle is 68cm. the length is 2cm less than 3 times the width. find the length and width.
P = 68 cm.
Width = x-cm.
Length = (3x - 2).
P = 2x + 2(3x-2) = 68 cm,
2x + 6x - 4 = 68,
8x = 72,
X = 9cm.
3x - 2 = 3*9 - 2 = 25cdm.
Oh, you've come to the right clown for a bit of mathematical fun! Let's clown around with this problem, shall we?
Let's start by assuming the width of our rectangle is "w" cm. According to the problem, the length is 2 cm less than 3 times the width, which we can write as 3w - 2 cm.
Now, the perimeter of a rectangle is calculated by adding up all its sides. Since we have two sides that are width (w) and two sides that are length (3w - 2), we can write the equation:
Perimeter = 2(w) + 2(3w - 2)
Since we know the perimeter is given as 68 cm, we can substitute it into the equation:
68 = 2w + 2(3w - 2)
Simplifying further:
68 = 2w + 6w - 4
68 = 8w - 4
Adding 4 on both sides:
72 = 8w
And dividing both sides by 8:
w = 9
Hooray! We found out the width! Now we can substitute it back into the expression for the length to find its value:
Length = 3(9) - 2
Length = 27 - 2
Length = 25
So, the width of the rectangle is 9 cm, and the length is 25 cm. Voila!
Now, if you need any clownish assistance with anything else, I'm here to entertain you!
Step 1: Let's assume the width of the rectangle is "w" cm.
Step 2: According to the problem, the length of the rectangle is 2 cm less than 3 times the width. So, the length is (3w - 2) cm.
Step 3: The formula for the perimeter of a rectangle is: P = 2(length + width)
Step 4: Substituting the values into the formula, we get: 68 = 2((3w - 2) + w)
Step 5: Simplifying the equation, we have: 68 = 2(4w - 2)
Step 6: Distributing 2 through the parentheses, we get: 68 = 8w - 4
Step 7: Adding 4 to both sides, we have: 72 = 8w
Step 8: Dividing both sides by 8, we get: w = 9
Step 9: Substitute the value of w back into the equation to find the length: length = 3w - 2 = 3(9) - 2 = 27 - 2 = 25
So, the width of the rectangle is 9 cm and the length is 25 cm.
To find the length and width of a rectangle given the perimeter and the relationship between the length and width, you can set up a system of equations.
Let's denote the width of the rectangle as 'w' and the length as 'l.'
According to the given information:
1. The perimeter of a rectangle is calculated by adding the lengths of all four sides. So we have:
Perimeter = 2 * (Length + Width)
Given Perimeter = 68 cm
Substituting in the variables:
68 = 2 * (l + w)
2. The length is 2 cm less than 3 times the width. So we can represent this as:
Length = 3 * Width - 2
Now, we can substitute the second equation into the first equation to solve for the width:
68 = 2 * ((3 * w - 2) + w)
To solve this equation algebraically, we simplify it:
68 = 2 * (4w - 2)
68 = 8w - 4
Adding 4 to both sides:
72 = 8w
Dividing both sides by 8:
9 = w
Now, we can substitute the value of the width back into the second equation to solve for the length:
Length = 3 * Width - 2
Length = 3 * 9 - 2
Length = 27 - 2
Length = 25
Therefore, the length of the rectangle is 25 cm, and the width is 9 cm.