Question

select the correct answer from the drop - down menu. chris is constructing a diagram for a deck he is restructuring in his backyard. the deck will be in the shape of a square, and he has labeled a side length with the equation below, where x represents the original deck area. side length = √(x + 12) according to his equation chris wants to drop - down options: increase the length of the deck by 12 feet; increase the perimeter of the deck by 12 feet; increase the perimeter of the deck by 48 feet; increase the area of the deck by 144 square feet; increase the area of the deck by 12 square feet; increase the width of the deck by 12 feet

Explanation:

1. Let the original side length be $s$. The original area $x = s^2$, so $s = \sqrt{x}$.
2. The new side length is $\sqrt{x + 12}$. The new area is $(\sqrt{x + 12})^2 = x + 12$.
3. Subtract the original area from the new area: $(x + 12) - x = 12$. This shows the area is increased by 12 square feet.
4. Eliminate other options:

• The change is not a fixed 12 ft to side length (new side is $\sqrt{x+12}$, not $\sqrt{x}+12$), so side/perimeter increases are not 12/48 ft.
• The area increase is 12, not 144, square feet.

Answer:

increase the area of the deck by 12 square feet