How would I figure out another rectangle equation? The length of a rectangle is 4 meters less than 3 times the width. The perimeter is 24 meters. Find the width.
P = 2 l + 2w
L = 3w-4
24 = 2(3w-4) + 2w
24 = 6w -8 + 2w
24 = 8w -8
24 + 8 = 8w-8 +8
32 = 8w
8w/8 = 32/8
w = 4
This is the answer I came up with and the website for my homework says it is wrong. I thought I was doing this equation wrong. Thank you.
To figure out the equation for this rectangle, we can follow a step-by-step process:
1. Let's start by assigning variables to the quantities mentioned in the problem. Let's use "L" for the length and "W" for the width of the rectangle.
2. The problem states that "the length of a rectangle is 4 meters less than 3 times the width." In equation form, this can be written as L = 3W - 4.
3. The problem also mentions that "the perimeter is 24 meters." The formula for the perimeter of a rectangle is P = 2L + 2W. Substituting the value for L from step 2, we get 24 = 2(3W - 4) + 2W.
4. Simplify the equation by distributing and combining like terms: 24 = 6W - 8 + 2W.
5. Combine like terms: 24 = 8W - 8.
6. Isolate the variable by adding 8 to both sides: 32 = 8W.
7. Solve for W by dividing both sides by 8: W = 4.
So, the width of the rectangle is 4 meters.