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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.

Verified Answer :

MissPhiladelphia

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

calculista

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

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