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.

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

Hello,

(x+9)(x+3=x²+21+27 No
(x-3)(x-9)=x²-12x+27 No

(x+18)(x+9)=x²+27x+162 Yes
(x-9)(x-18)=x²-27x+162 No

Answer C

Answer 2

we have

$x^{2} + 27x + 162$

Using a graph tool------> to resolve the second order equation

the solution is

$x=-18\\ x=-9$

so

$x^{2} + 27x + 162=(x+18)*(x+9)$

therefore

the answer is the option

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