The length of a rectangle is four times its width. If the perimeter of the rectangle is 80yd, find its area.

Well, well, well, looks like we have ourselves a math problem! Let's give it a whirl.

First things first, let's assign some names to these mysterious dimensions. Let's call the width "W" (because it's a "W"onderful dimension) and the length "L" (which stands for "Long and lovely").

We know that the length is four times the width, so L = 4W.

Now, the perimeter of a rectangle is calculated by adding up all the sides. In this case, we have two sides of length W and two sides of length L.

So, the equation for the perimeter is: 2W + 2L = 80yd.

But fear not, my friend, we can substitute L with 4W and simplify the equation:
2W + 2(4W) = 80

Now, we can solve for W. 2W + 8W = 80
10W = 80
W = 8yd

Now that we know the width, we can easily find the length by substituting it back into L = 4W. L = 4(8) = 32yd.

Ah, but we're not done yet! The area of a rectangle is calculated by multiplying the length by the width. So, in this case, the area is: 8yd * 32yd = 256yd².

Ta-da! The area of this rectangle is 256 square yards. I hope that didn't leave you feeling too square!

Let's begin by assigning variables to the length and width of the rectangle. Let's say that the width of the rectangle is represented by "W" and the length is represented by "L".

Based on the given information, we know that the length of the rectangle is four times its width. We can express this relationship as:

L = 4W

Next, we are told that the perimeter of the rectangle is 80 yards. The formula for the perimeter of a rectangle is given by:

Perimeter = 2(L + W)

Substituting the given values, we have:

80 = 2(L + W)

Now, let's substitute L with 4W:

80 = 2(4W + W)

Expanding the equation, we get:

80 = 2(5W)

Simplifying further:

80 = 10W

Now, we can solve for W by dividing both sides of the equation by 10:

W = 80/10

W = 8

Therefore, the width of the rectangle is 8 yards. To find the length, we can substitute the value of W into the equation L = 4W:

L = 4(8) = 32

So, the length of the rectangle is 32 yards.

Finally, to find the area of the rectangle, we use the formula:

Area = Length x Width

Area = 32 x 8

Area = 256 square yards

Hence, the area of the rectangle is 256 square yards.

To find the area of a rectangle, we need to know its length and width. The problem tells us that the length is four times the width.

Let's use the variable "x" to represent the width of the rectangle. So, the length would be 4x.

The formula for the perimeter of a rectangle is P = 2(length + width).

In this case, we have P = 80 yd.

Substituting the values into the formula, we can write:

80 = 2(4x + x)

Now, we can solve for x:

80 = 2(5x)
80 = 10x
x = 8 yd

Now that we know the width is 8 yd, we can find the length by multiplying it by 4:

Length = 4 * 8 = 32 yd

To find the area of the rectangle, we use the formula A = length * width:

Area = 32 yd * 8 yd = 256 yd²

So, the area of the rectangle is 256 square yards.

2(w + 4w) = 80

w = 8
area = 8 * 4*8 = 256 yd^2