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.

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

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calculista calculista · Answer 2 · 2018-08-30T00:12:52+02:00

we need to factor the expression

[tex] x^{2} + 27x + 162 [/tex]

Equate to zero the expression

[tex] x^{2} + 27x + 162=0 [/tex]

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

[tex] x^{2} + 27x =-162 [/tex]

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

[tex] x^{2} + 27x +182.25=-162+182.25 [/tex]

[tex] x^{2} + 27x +182.25=20.25 [/tex]

Rewrite as perfect squares

[tex] (x+13.5)^{2}=20.25 [/tex]

[tex] (x+13.5)=(+/-)4.5 [/tex]

[tex] x1=-13.5+4.5= -9 [/tex]

[tex] x2=-13.5-4.5= -18 [/tex]

Hence

[tex] x^{2} + 27x + 162 =(x+9)*(x+18) [/tex]

Remember that the area of the rectangle is equal to

[tex] A=L*W [/tex]

therefore

the answer is

the dimensions of the rectangular piece of cloth could be

[tex] L=(x+18)\ inches\\ W=(x+9)\ inches [/tex]