Answer:
\(x^{2}+3x-1 meters\)
Step-by-step explanation:
Given : Area of rectangle : \(x^{3} +5x^{2} +5x-2\)
Width : \(x+2\)
To Find : Length
Solution :
Formula of area of rectangle : \(Length \times Width\)
Substituting the given values in formula to calculate Length.
\(x^{3} +5x^{2} +5x-2=Length \times (x+2)\)
\(\frac{x^{3} +5x^{2} +5x-2}{x+2} = Length\) ---(A)
Solving this equation using Formula :
Dividend = (Divisor * Quotient) +Remainder
Since dividend is \(x^{3} +5x^{2} +5x-2\)
Divisor is \(x+2\)
Thus ,
⇒ \(x^{3} +5x^{2} +5x-2=[(x+2)*x^{2}] +(3x^{2} +5x-2)\)
⇒ \(x^{3} +5x^{2} +5x-2=[(x+2)*(x^{2}+3x)] +(-x-2)\)
⇒\(x^{3} +5x^{2} +5x-2=[(x+2)*(x^{2}+3x-1)] +0\)
Thus the quotient is \(x^{2}+3x-1\)
So, A becomes
\(\frac{x^{3} +5x^{2} +5x-2}{x+2} = Length\)
\(x^{2}+3x-1 = Length\)
Hence Length of Rectangle is \(x^{2}+3x-1 meters\)
