Question

Yasmin is building a square coffee table to nest inside an existing table. The larger table has side lengths 2x + 6ft.The nested table will have
side lengths 1/4 the length of the existing lengths. What is the area of the new table top?
x2 +
ft2​

Answer 1

We have been given that Yasmin is building a square coffee table to nest inside an existing table. The larger table has side lengths $2x + 6$ 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 $2x + 6$ as:

$\text{Side of nested table}=\frac{1}{4}\times (2x+6)$

$\text{Side of nested table}=\frac{1}{4}\times 2(x+3)$

$\text{Side of nested table}=\frac{x+3}{2}$

We know that area of square is square of its side length.

$\text{Area of nested table}=(\frac{x+3}{2})^2$

$\text{Area of nested table}=\frac{(x+3)^2}{2^2}$

$\text{Area of nested table}=\frac{x^2+6x+9}{4}$

Therefore, the area of nested table is $\frac{x^2+6x+9}{4}$ square feet.