The length of a rectangle is 4 times the width. The area is 900 square centimeters. Find the length and width of the rectangle

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Width = W.

Length = 4W.
Area = W * 4W = 900 cm^2.
W * 4W = 900.
W = ?

w

To find the length and width of the rectangle, we can set up a system of equations based on the given information:

Let's assume the width of the rectangle is 'w' centimeters.

According to the given information, the length of the rectangle is 4 times the width. So, the length can be represented as 'l = 4w'.

The formula for the area of a rectangle is 'A = length * width'. Substituting the given values, we have:

900 = (4w) * w

To solve this equation for 'w', we can either multiply the terms inside the brackets or use the distributive property.

900 = 4w^2

Now, let's arrange the equation in standard quadratic form:

4w^2 = 900

To isolate 'w', divide both sides of the equation by 4:

w^2 = 900 / 4

w^2 = 225

Taking the square root of both sides to solve for 'w', we get:

w = √225

w = 15

Since we assumed the width to be 'w', the width of the rectangle is 15 centimeters.

Now, substitute the value of 'w' back into the equation for length:

l = 4w
l = 4 * 15
l = 60

Therefore, the length of the rectangle is 60 centimeters.