the perimeter of a rectangle is 3.5 times the legth. the width is 2.5cm less than the legth. what is the width?

2L + 2W = 3.5 L

L - W = 2.5

1.5L - 2W = 0
L = (4/3) W

W/3 = 2.5 cm
W = 7.5 cm
L = 10 cm

Let's assume the length of the rectangle is 'L' cm.

According to the given information, the perimeter of the rectangle is 3.5 times the length, which can be expressed as:

Perimeter = 3.5L

Now, it is also mentioned that the width is 2.5 cm less than the length, which can be expressed as:

Width = L - 2.5

The perimeter of a rectangle is calculated by adding all sides, so it can be represented as:

Perimeter = 2 × (Length + Width)

Since the length is 'L' and the width is L - 2.5, we can substitute these values into the perimeter equation:

3.5L = 2 × (L + (L - 2.5))

Simplifying this equation will help us find the value of the length:

3.5L = 2 × (2L - 2.5)

Now, solve for L:

3.5L = 4L - 5

3.5L - 4L = -5

-L = -5

L = 5

Therefore, the length of the rectangle is 5 cm.

Now we can find the width by substituting L = 5 into the equation for the width:

Width = L - 2.5 = 5 - 2.5 = 2.5

Hence, the width of the rectangle is 2.5 cm.

To find the width of the rectangle, we need to use the given information about its perimeter and the relationship between the length and width.

Let's start by assigning variables to the unknown quantities:
Let L be the length of the rectangle.
Let W be the width of the rectangle.

Given:
The perimeter of the rectangle is 3.5 times the length: P = 3.5L.
The width is 2.5cm less than the length: W = L - 2.5.

The perimeter of a rectangle is given by the formula: P = 2(L + W).
By substituting the given values, we can write the equation as:
3.5L = 2(L + (L - 2.5)).

Simplifying the equation:
3.5L = 2(2L - 2.5)
3.5L = 4L - 5.

Now we solve for L:
3.5L - 4L = -5,
-0.5L = -5,
L = -5 / -0.5,
L = 10.

Now that we have found the value of L, we can substitute it back into the equation for W:
W = L - 2.5,
W = 10 - 2.5,
W = 7.5.

Therefore, the width of the rectangle is 7.5 cm.