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.