the perimeter of a rectangle is 46 feet. The width is 3ft less than twice the length. find the length and width of the rectangle

Using w and h for width and length, we know:

2(w+h) = 46
w = 2h-3

So, 2(2h-3+h) = 46
2(3h-3) = 46
6h-6 = 46
6h = 52
h = 8 2/3
w = 14 1/3

Why did the rectangle go on a diet? Because it wants to minimize its perimeter! Let's solve this puzzling problem together.

Let's call the length of the rectangle "L" and the width "W." From the given information, we know that the perimeter, which is the sum of all sides, is equal to 46 feet.

So, the equation for the perimeter is:

2L + 2W = 46

But we also know that the width is 3 feet less than twice the length. In other words:

W = 2L - 3

Now, let's substitute the value of W from the second equation into the first equation:

2L + 2(2L - 3) = 46

Simplifying:

2L + 4L - 6 = 46

Combining like terms:

6L - 6 = 46

Now, let's isolate L by adding 6 to both sides:

6L = 52

Dividing both sides by 6:

L = 8.67

Now, let's substitute the value of L back into the equation for W:

W = 2(8.67) - 3

W ≈ 14.34

Therefore, the length of the rectangle is approximately 8.67 feet and the width is approximately 14.34 feet. Keep in mind that we rounded the width, so it might have a funny decimal.

Let's solve this step-by-step.

Step 1: Let's assume the length of the rectangle is l.

Step 2: According to the problem, the width is 3 feet less than twice the length. So, the width would be (2l - 3).

Step 3: The formula to find the perimeter of a rectangle is P = 2(l + w), where P is the perimeter, l is the length, and w is the width.

Step 4: Given that the perimeter of the rectangle is 46 feet, we can now write the equation:
46 = 2(l + (2l - 3))

Step 5: Simplify the equation:
46 = 2(3l - 3)
23 = 3l - 3 (Dividing both sides by 2)

Step 6: Add 3 to both sides of the equation:
26 = 3l

Step 7: Divide both sides of the equation by 3 to solve for l:
l = 26/3

Step 8: Simplify the value of l:
l ≈ 8.67 feet

Step 9: Now let's find the width using the value of l:
w = 2l - 3
w = 2(8.67) - 3
w ≈ 14.34 feet

Therefore, the length of the rectangle is approximately 8.67 feet, and the width is approximately 14.34 feet.

To find the length and width of the rectangle, we can use the given information and set up an equation.

Let's assume that the length of the rectangle is represented by "L" and the width is represented by "W".

From the problem, we know that the perimeter of a rectangle is calculated by adding up all its sides. Since a rectangle has two pairs of equal sides, the perimeter can be expressed as: P = 2L + 2W.

The problem also states that the width is 3 feet less than twice the length. So, we can set up another equation: W = 2L - 3.

Now, we can substitute the second equation into the first equation to solve for the length (L).

P = 2L + 2W
46 = 2L + 2(2L - 3)
46 = 2L + 4L - 6 (distribute the 2 to 2L and -3)
46 = 6L - 6 (combine like terms -2L and 4L)
6L = 46 + 6
6L = 52 (add 46 and 6)
L = 52 / 6
L = 8.67 feet

Now, let's substitute the value of L back into the second equation to solve for the width (W).

W = 2L - 3
W = 2(8.67) - 3
W = 17.34 - 3
W = 14.34 feet

Therefore, the length of the rectangle is approximately 8.67 feet, and the width is approximately 14.34 feet.