The length of a rectangle is 3 yards less than 3 times the width. If the perimeter is 50 yards, find the length and the width of the rectangle.
Ah, the mysterious rectangle! Let's solve this riddle together!
Let's assume the width of the rectangle is "w" yards. Now if the length is 3 yards less than 3 times the width, then the length would be 3w - 3 yards.
Now, we know that the perimeter of any rectangle is calculated by adding up all the sides. In this case, the perimeter is given as 50 yards. So, let's set up an equation to represent that:
2(length) + 2(width) = perimeter
Now let's plug in the values we have:
2(3w - 3) + 2w = 50
Simplify that a bit:
6w - 6 + 2w = 50
Combine like terms:
8w - 6 = 50
Add 6 to both sides:
8w = 56
Divide both sides by 8:
w = 7
So, the width of the rectangle is 7 yards.
Now let's find the length by substituting the value of width back into our earlier equation:
length = 3w - 3
length = 3(7) - 3
length = 21 - 3
length = 18
So, the length of the rectangle is 18 yards.
To recap, the width is 7 yards and the length is 18 yards. Voila!
Let's solve this step by step.
1. Let's assume the width of the rectangle is "x" yards.
2. The length of the rectangle is given as "3 times the width minus 3 yards," which can be written as: 3x - 3.
3. The formula for the perimeter of a rectangle is: 2(length + width).
4. Substituting the given values into the formula, we get: 2((3x - 3) + x) = 50.
5. Simplifying the equation, we have: 2(4x - 3) = 50.
6. Expanding the equation further, we get: 8x - 6 = 50.
7. Adding 6 to both sides of the equation, we have: 8x = 56.
8. Dividing both sides by 8, we get: x = 7.
So, the width of the rectangle is 7 yards.
9. Substituting the value of x back into the equation for the length, we get: 3(7) - 3 = 21 - 3 = 18.
Therefore, the length of the rectangle is 18 yards.
To summarize:
The width of the rectangle is 7 yards, and the length is 18 yards.
To solve this problem, we can start by assigning variables to the length and width of the rectangle. Let's use "L" for length and "W" for width.
According to the information given, the length of the rectangle is 3 yards less than 3 times the width. In equation form, this would be:
L = 3W - 3
Next, we know that the perimeter of a rectangle is calculated by adding all four sides. In this case, the perimeter is given as 50 yards:
Perimeter = 2L + 2W = 50
Now we can substitute the expression for length (L) from the first equation into the second equation and solve for the width (W):
2(3W - 3) + 2W = 50
6W - 6 + 2W = 50
8W - 6 = 50
8W = 56
W = 7
By substituting the obtained value of W into the first equation, we can find the length (L):
L = 3(7) - 3
L = 21 - 3
L = 18
Therefore, the length of the rectangle is 18 yards and the width is 7 yards.
P = 2L + 2W
50 = 2(3W - 3) + 2W
50 = 6W - 6 + 2W
Take it from there.