Question

A rectangle has an area of x3 + 5x2 + 5x – 2 square meters and a width of x + 2 meters. Find its length.

A) x2 + 5x – 4 meters
B) x2 +3x – 1 meters
C) x2 + 7x – 9 meters
D) x2 + 3x + 1 meters

Answer 1

The solution to the problem is as follows:

A = l * w 

l = A/w 

= (x^3 + 5x^2 + 5x - 2) / (x + 2) 

= [(x^2 + 3x - 1)(x + 2)] / (x + 2) 

= x^2 + 3x - 1

I hope my answer has come to your help. God bless and have a nice day ahead!

Answer 2

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  $x^{2}+3x-1 meters$