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Sagot :
The length of rectangle is (x - 5).
We are given-
Area of rectangle = [tex]x^{3} - 5x^{2} + 3x - 15[/tex]
Width of rectangle = [tex]x^{2} + 3[/tex]
Using the formula, the length will be calculated by rewriting the formula as -
Length = Area/width
Keep the values in formula to find the length of rectangle.
Length = [tex]\frac{x^{3} - 5x^{2} + 3x - 15}{x^{2} + 3}[/tex]
In numerator, separating the common values and rewriting the equation -
Length = [tex]\frac{x^{2} (x - 5) +3 (x - 5)}{x^{2} + 3}[/tex]
Rewriting the equation to for ease of solving to find the length of rectangle -
Length = [tex]\frac{(x^{2} +3)(x - 5)}{(x^{2} +3)}[/tex]
Cancelling [tex](x^{2} + 3)[/tex] as it is common in both numerator and denominator. Now, we will get the value of length of rectangle.
Length = (x - 5)
Hence, the length of rectangle is (x - 5).
The complete question is -
The area of a rectangle is [tex]x^{3} - 5x^{2} + 3x - 15[/tex], and the width of the rectangle is [tex]x^{2} + 3[/tex]. If area = length × width, what is the length of the rectangle? x + 5 x – 15 x + 15 x – 5
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