The width of a rectangle is 25% of the length. The perimeter is 250 cm. Find the width and the length of the rectangle.

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To solve this problem, let's start by assigning variables to the width and length of the rectangle. Let's use "w" for width and "l" for length.

According to the problem, the width of the rectangle is 25% of the length. We can express this as an equation: w = 0.25 * l.

The perimeter of a rectangle is given by the formula P = 2(l + w), where P is the perimeter, l is the length, and w is the width. In this case, the perimeter is 250 cm, so we have the equation 250 = 2(l + w).

Now we have a system of two equations:

w = 0.25 * l
250 = 2(l + w)

To find the width and length, we can substitute the first equation into the second equation, and solve for l:

250 = 2(l + 0.25 * l)
250 = 2(1.25 * l)
250 = 2.5 * l
l = 100

Now that we have the length, we can substitute this value into the first equation to find the width:

w = 0.25 * l
w = 0.25 * 100
w = 25

Therefore, the width of the rectangle is 25 cm, and the length is 100 cm.

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

According to the given information, the width of the rectangle is 25% of the length, which means the width is 0.25L cm.

The perimeter of a rectangle is calculated by summing up the lengths of all four sides. In this case, the perimeter is given as 250 cm.

Since the rectangle has two pairs of equal sides (the length and the width), we can express the perimeter as:
2(length) + 2(width) = 250 cm.

Substituting the values of the length and width into the equation, we have:
2(L) + 2(0.25L) = 250 cm.

Simplifying the equation, we get:
2L + 0.5L = 250 cm.

Combining like terms, we get:
2.5L = 250 cm.

Dividing both sides of the equation by 2.5, we find:
L = 250 cm / 2.5 = 100 cm.

Therefore, the length of the rectangle is 100 cm.

Substituting the value of the length into the equation for the width, we have:
Width = 0.25L = 0.25(100 cm) = 25 cm.

Therefore, the width of the rectangle is 25 cm.