Question

A piece of cloth is folded into a square with a side length measuring x inches. When it is unfolded, it has an area of x2 + 27x + 162 square inches.

Which could be the dimensions of the rectangular piece of cloth when it is unfolded? Remember, the area of a rectangle can be determined using the formula A = lw.

Answer 1

we need to factor the expression

`x^(2) + 27x + 162`

Equate to zero the expression

`x^(2) + 27x + 162=0`

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`x^(2) + 27x =-162`

Complete the square. Remember to balance the equation by adding the same constants to each side

`x^(2) + 27x +182.25=-162+182.25`

`x^(2) + 27x +182.25=20.25`

Rewrite as perfect squares

`(x+13.5)^(2)=20.25`

`(x+13.5)=(+/-)4.5`

`x1=-13.5+4.5= -9`

`x2=-13.5-4.5= -18`

Hence

`x^(2) + 27x + 162 =(x+9)*(x+18)`

Remember that the area of the rectangle is equal to

`A=L*W`

therefore

the answer is

the dimensions of the rectangular piece of cloth could be

`L=(x+18)\ inches\\ W=(x+9)\ inches`

Answer 2

A piece of cloth is folded into a square with a side length measuring x inches. When it is unfolded, it has an area of x2 + 27x + 162 square inches. Since the area for square is x times x then equate the given equation to the area fomula.

(x2 + 27x + 162) = 0
(x + 9) (x + 18) = 0
The dimensions are 9 and 18