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.
Please answer ..
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.

length = (x + 9) inches and width = (x + 3) inches
length = (x − 3) inches and width = (x − 9) inches
length = (x + 18) inches and width = (x + 9) inches
length = (x − 9) inches and width = (x − 18) inches

Answer 1

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) = 0The dimensions are 9 and 18
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Answer 2

Answer:

C. Length is (x+18) inches and width is (x+9) inches.

Step-by-step explanation:

We know that the side of the cloth is 'x' inches.

As, the area of the cloth is $x^{2}+27x+162$.

Equating the polynomial by 0, we will find the roots of the equation.

i.e. $x^{2}+27x+162=0$

Solution of the quadratic equation is given by,

$x=\frac{-27\pm \sqrt{27^{2}-4\times 1\times 162}}{2\times 1}$

i.e. $x=\frac{-27\pm \sqrt{729-648}}{2}$

i.e. $x=\frac{-27\pm \sqrt{81}}{2}$

i.e. $x=\frac{-27+9}{2}$ and $x=\frac{-27-9}{2}$

i.e. $x=\frac{-18}{2}$ and $x=\frac{-36}{2}$

i.e. x= -9 and x= -18

As, the area of rectangle is L × W.

So, we have the area of the cloth is $(x+9)(x+18)$.

Thus, the length is (x+18) inches and width is (x+9) inches.