The area of a rectangle is 532 square units. Find the length and the width of the rectangle.

One side of the rectangle is x+5 and the other is x-4

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(x+5)*(x-4)=532

x^2+x-20=532
x^2+x-552=0

(x-23)*(x+24)=0

x=23, so length, width is 23-4, and 23-5

oops, 23-4, and 23+5

To find the length and width of the rectangle, we need to set up an equation using the area of a rectangle formula.

The formula for the area of a rectangle is:

Area = Length × Width

Given that one side of the rectangle is x+5 and the other side is x-4, we can set up the equation:

(x+5)(x-4) = 532

To solve this equation, we can expand the expression on the left side:

x^2 - 4x + 5x - 20 = 532

Combining like terms, we get:

x^2 + x - 20 = 532

Moving all the terms to one side of the equation, we have:

x^2 + x - 20 - 532 = 0

Simplifying further:

x^2 + x - 552 = 0

To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. Let's use factoring:

(x - 16)(x + 34) = 0

Setting each factor equal to zero:

x - 16 = 0 or x + 34 = 0

Solving these equations, we get:

x = 16 or x = -34

Since the length and width of a rectangle cannot be negative, we can discard the solution x = -34.

Now that we have x = 16, we can substitute it back into the expressions for the length and width:

Length = x + 5 = 16 + 5 = 21 units
Width = x - 4 = 16 - 4 = 12 units

Therefore, the length of the rectangle is 21 units and the width is 12 units.