Answer:
The original side length is 2. The area of the original square is 4.
This means the new side length, x+6, would be 8. The area of the new square is 64.
Step-by-step explanation:
If you want to know what the length of the side is, here is how you solve it:
x is the side length
therefore, [tex]x^{2}[/tex] is the area
if x+6 becomes the length and the area of this is 16[tex]x^{2}[/tex]
then we can say that [tex](x+6)^{2} = 16x^{2}[/tex]
we can expand this to become [tex]x^{2} + 12x +36=16x^{2}[/tex]
which becomes [tex]-15x^{2} +12x +36=0[/tex]
If we factor it, we get [tex](-15x^{2} + 30x)(-18x+36)=0[/tex]
[tex]-15x(x-2)-18(x-2)=0[/tex]
[tex](-15x-18)(x-2)=0[/tex]
[tex]x=2\\or\x=-\frac{6}{5}[/tex]
because length cannot be a negative number, the only option for the original side length is 2. The area of the original square is 4.
This means the new side length, x+6, would be 8. The area of the new square is 64.
