The ratio of the width to the length of a rectangle is 4:5, If the area of the rectangle is 500 square centimeters, what is the length of the rectangle?

w L = 500

L = 5 w/4

w(5w/4) = 500

w^2 = 400

w = 20
L = (5/4)20 = 25

To solve this problem, we need to find the length of the rectangle.

Let's assume the width of the rectangle is 4x, and the length is 5x (as given in the ratio).

The formula for calculating the area of a rectangle is given by:
Area = Length x Width

So, let's substitute the values into the equation:

Area = (5x) x (4x)

Given that the area is 500 square centimeters, we can set up the equation:

500 = 5x * 4x

Simplifying further:
500 = 20x^2

Now, let's divide both sides of the equation by 20:
500/20 = 20x^2/20

25 = x^2

To isolate x, we need to take the square root of both sides:
√25 = √x^2

Taking the square root:
5 = x

So, the value of x is 5.

Now, to find the length of the rectangle, we substitute x back into the length (5x):
Length = 5 * 5
Length = 25

Therefore, the length of the rectangle is 25 centimeters.

To find the length of the rectangle, we first need to set up an equation using the given information.

Let's assume the width of the rectangle is 4x and the length is 5x, where x is a common factor.

The area of a rectangle is given by the formula: Area = Length * Width.

Substituting the values: 500 = (5x) * (4x)

To solve this equation, we can rearrange it to get the quadratic equation: 20x^2 = 500

Divide both sides of the equation by 20: x^2 = 25

Taking the square root of both sides: x = ±√25

Therefore, x can be either +5 or -5. However, since we are dealing with physical dimensions, we consider only the positive value.

So, x = 5.

Now, substituting this value back into our assumptions, we find that the length of the rectangle is 5x, which is 5 * 5 = 25 centimeters.