Respuesta :
We have been given that Yasmin is building a square coffee table to nest inside an existing table. The larger table has side lengths [tex]2x + 6[/tex] ft.The nested table will have side lengths 1/4 the length of the existing lengths.
First of all, we will find side length of nested table by finding 1/4 of [tex]2x + 6[/tex] as:
[tex]\text{Side of nested table}=\frac{1}{4}\times (2x+6)[/tex]
[tex]\text{Side of nested table}=\frac{1}{4}\times 2(x+3)[/tex]
[tex]\text{Side of nested table}=\frac{x+3}{2}[/tex]
We know that area of square is square of its side length.
[tex]\text{Area of nested table}=(\frac{x+3}{2})^2[/tex]
[tex]\text{Area of nested table}=\frac{(x+3)^2}{2^2}[/tex]
[tex]\text{Area of nested table}=\frac{x^2+6x+9}{4}[/tex]
Therefore, the area of nested table is [tex]\frac{x^2+6x+9}{4}[/tex] square feet.
