The length of a rectangle is four times its width. If the perimeter of the rectangle is 50cm. find its area.

how do i set this up?

(2 * 4w) + 2w = 50

Solve for the width (w).

Then multiply the length and the width to get the area.

To set up this problem, you need to understand two important formulas: the formula for the perimeter of a rectangle and the formula for the area of a rectangle.

1. Perimeter of a rectangle: The perimeter of a rectangle is the sum of the lengths of all its sides. For a rectangle, the formula is P = 2L + 2W, where P represents the perimeter, L represents the length, and W represents the width.

2. Area of a rectangle: The area of a rectangle is the product of its length and width. The formula is A = L * W, where A represents the area, L represents the length, and W represents the width.

Now let's go ahead and set up the problem using the given information:

1. The length of the rectangle is four times its width. Let's represent the width as W. Therefore, the length is 4W.

2. The perimeter of the rectangle is given as 50 cm. So using the perimeter formula, we have:
P = 2L + 2W
50 = 2(4W) + 2W

Simplifying the equation, we get:
50 = 8W + 2W

Combining like terms, we have:
50 = 10W

Now, let's solve for W by dividing both sides of the equation by 10:
50/10 = W
5 = W

Now that we know the width is 5 cm, we can find the length by multiplying it by 4:
L = 4W = 4 * 5 = 20 cm

Finally, let's calculate the area of the rectangle using the area formula:
A = L * W = 20cm * 5cm = 100 cm²

Therefore, the area of the rectangle is 100 square cm.