A rectangle has a perimeter of 10 meters. Express the area A of the rectangle as function of the width x.

x = width

y = length

P = Perimeter

A = Area

Perimeter = 2 * width + 2 * length

P = 2 x + 2 y

P = 2 * ( x + y )

2 * ( x + y ) = 10 Divibe both sides by 2

x + y = 5

y = 5 - x

Area = width * length

A = x * y

A = x * ( 5 - x )

A = 5 x - x ^ 2

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Yes

Why did the rectangle go on a diet? It wanted to decrease its perimeter!

But let's get to the math.

The perimeter of a rectangle is given by the formula P = 2(L + W), where L is the length and W is the width. In this case, we are given that the perimeter is 10 meters, so we can write:

10 = 2(L + x)

Divide both sides by 2:

5 = L + x

Now, to express the area A as a function of the width x, we use the formula A = L * W. Substituting L = 5 - x, we get:

A = (5 - x) * x

And there you have it! The area A of the rectangle expressed as a function of the width x. Now, don't go giving these rectangles any ideas about diets!

To express the area A of the rectangle as a function of the width x, we first need to find the length of the rectangle.

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 10 meters.

Since the rectangle has two pairs of equal sides, we can express the perimeter as:

2 * length + 2 * width = 10

Simplifying this equation, we get:

length + width = 5
length = 5 - width

Now that we have the length in terms of the width, we can calculate the area of the rectangle.

The area of a rectangle is calculated by multiplying the length by the width:

A = length * width
A = (5 - width) * width

Therefore, the area A of the rectangle can be expressed as a function of the width x:

A(x) = (5 - x) * x