Suppose that the width of a certain rectangle is three-fourths of its length, and the area of that same rectangle is 108 square meters. Find the length and the width of the rectangle

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To find the length and width of the rectangle, we can use the information given in the problem. Let's define the length of the rectangle as 'L' and the width as 'W'.

According to the problem, the width of the rectangle is three-fourths of its length. This can be expressed as:
W = (3/4)L

The area of the rectangle is given as 108 square meters. The formula for the area of a rectangle is:
Area = Length x Width

Substituting the values we know into the formula, we get:
108 = L * W

Now, we can substitute the value of W in terms of L from the first equation into the second equation:
108 = L * ((3/4)L)

Simplifying, we get:
108 = (3/4)L^2

To solve for L, we can rearrange the equation as follows:
L^2 = (108 * 4)/3
L^2 = 432/3
L^2 = 144

Taking the square root of both sides, we find:
L = √144
L = 12

Now that we have found the length, we can substitute it back into the first equation to find the width:
W = (3/4)L
W = (3/4) * 12
W = 9

Therefore, the length of the rectangle is 12 meters and the width is 9 meters.