Solve by setting up the proper equation to describe the facts given and then carrying out the mathematical calculations to solve for the unknown variable(s).
The length of a rectangle is 3 times the width. The difference between the length and the width is 8 feet. Determine the rectangle’s length
let the width be x
then the length is 3x
3x - x = 8
2x = 8
x = 4
width is 4 ft
length is 12 ft
Oh, a rectangle riddle! Let's solve it together, shall we?
Let's call the width of the rectangle 'w'. According to the given information, the length of the rectangle is 3 times the width, so the length is 3w.
We also know that the difference between the length and the width is 8 feet. So, we can set up the equation:
3w - w = 8
Now we can solve it:
2w = 8
w = 4
So the width of the rectangle is 4 feet. Since the length is 3 times the width, we can find the length:
length = 3w = 3 * 4 = 12
Ta-da! The length of the rectangle is 12 feet.
Let's solve this step-by-step:
1. Let's assume the width of the rectangle as 'w'.
2. According to the given information, the length of the rectangle is 3 times the width, so the length would be 3w.
3. The difference between the length and the width is 8 feet, which can be written as: length - width = 8.
4. Substituting the values of length and width from steps 2 and 1 into the equation, we get: 3w - w = 8.
5. Simplifying the equation, we get: 2w = 8.
6. Dividing both sides of the equation by 2, we get: w = 4.
7. So, the width of the rectangle is 4 feet.
8. Now, to find the length, substitute the value of width from step 7 into the equation of the length: length = 3w = 3 * 4 = 12.
9. Therefore, the rectangle's length is 12 feet.
So, the length of the rectangle is 12 feet.
To solve this problem, let's start by assigning variables to the unknowns in the problem. Let's denote the length of the rectangle as "L" and the width as "W".
According to the given information, the length of the rectangle is 3 times the width. We can write this as an equation:
L = 3W
The problem also tells us that the difference between the length and the width is 8 feet. Mathematically, this can be expressed as:
L - W = 8
Now we have a system of two equations with two variables. We can solve this system using substitution or elimination. Let's use substitution to solve for L:
Substituting the value of L from the first equation (L = 3W) into the second equation, we get:
3W - W = 8
Simplifying the equation, we have:
2W = 8
Divide both sides by 2 to solve for W:
W = 4
Now that we have the value of W, we can substitute it back into the first equation to find the value of L:
L = 3W = 3(4) = 12
Therefore, the length of the rectangle is 12 feet.