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

`x^(2)+3x-1 meters`

Explanation:

Given : Area of rectangle :
`x^(3) +5x^(2) +5x-2`

Width :
`x+2`

To Find : Length

Solution :

Formula of area of rectangle :
`Length * Width`

Substituting the given values in formula to calculate Length.

`x^(3) +5x^(2) +5x-2=Length * (x+2)`

`(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

`(x^(3) +5x^(2) +5x-2)/(x+2) = Length`

`x^(2)+3x-1 = Length`

Hence Length of Rectangle is
`x^(2)+3x-1 meters`

Answer 2

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!