Let's denote the increase in each dimension by $ x $ feet.

The original dimensions of the deck are 11 feet by 22 feet. Therefore, the original area of the deck is:
$$ 11 \times 22 = 242 \text{ square feet} $$

Khloe wants to triple the area of the deck. So, the new area should be:
$$ 3 \times 242 = 726 \text{ square feet} $$

The new dimensions of the deck will be:
$$ (11 + x) \text{ feet} $$
$$ (22 + x) \text{ feet} $$

The area of the new deck will be:
$$ (11 + x)(22 + x) $$

We need this area to be equal to 726 square feet:
$$ (11 + x)(22 + x) = 726 $$

Expanding the left-hand side, we get:
$$ 11 \times 22 + 11x + 22x + x^2 = 726 $$
$$ 242 + 33x + x^2 = 726 $$

Subtracting 726 from both sides, we get:
$$ x^2 + 33x + 242 - 726 = 0 $$
$$ x^2 + 33x - 484 = 0 $$

This is a quadratic equation. We can solve it using the quadratic formula:
$$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$

Here, $ a = 1 $, $ b = 33 $, and $ c = -484 $. Plugging these values into the quadratic formula, we get:
$$ x = \frac{-33 \pm \sqrt{33^2 - 4 \times 1 \times -484}}{2 \times 1} $$
$$ x = \frac{-33 \pm \sqrt{1089 + 1936}}{2} $$
$$ x = \frac{-33 \pm \sqrt{3025}}{2} $$
$$ x = \frac{-33 \pm 55}{2} $$

This gives us two solutions:
$$ x = \frac{-33 + 55}{2} = \frac{22}{2} = 11 $$
$$ x = \frac{-33 - 55}{2} = \frac{-88}{2} = -44 $$

Since $ x $ represents a length, it cannot be negative. Therefore, the only valid solution is:
$$ x = 11 $$

Khloe should increase each dimension by 11 feet.

Question

Let's denote the increase in each dimension by $ x $ feet.

The original dimensions of the deck are 11 feet by 22 feet. Therefore, the original area of the deck is:
$$ 11 \times 22 = 242 \text{ square feet} $$

Khloe wants to triple the area of the deck. So, the new area should be:
$$ 3 \times 242 = 726 \text{ square feet} $$

The new dimensions of the deck will be:
$$ (11 + x) \text{ feet} $$
$$ (22 + x) \text{ feet} $$

The area of the new deck will be:
$$ (11 + x)(22 + x) $$

We need this area to be equal to 726 square feet:
$$ (11 + x)(22 + x) = 726 $$

Expanding the left-hand side, we get:
$$ 11 \times 22 + 11x + 22x + x^2 = 726 $$
$$ 242 + 33x + x^2 = 726 $$

Subtracting 726 from both sides, we get:
$$ x^2 + 33x + 242 - 726 = 0 $$
$$ x^2 + 33x - 484 = 0 $$

This is a quadratic equation. We can solve it using the quadratic formula:
$$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$

Here, $ a = 1 $, $ b = 33 $, and $ c = -484 $. Plugging these values into the quadratic formula, we get:
$$ x = \frac{-33 \pm \sqrt{33^2 - 4 \times 1 \times -484}}{2 \times 1} $$
$$ x = \frac{-33 \pm \sqrt{1089 + 1936}}{2} $$
$$ x = \frac{-33 \pm \sqrt{3025}}{2} $$
$$ x = \frac{-33 \pm 55}{2} $$

This gives us two solutions:
$$ x = \frac{-33 + 55}{2} = \frac{22}{2} = 11 $$
$$ x = \frac{-33 - 55}{2} = \frac{-88}{2} = -44 $$

Since $ x $ represents a length, it cannot be negative. Therefore, the only valid solution is:
$$ x = 11 $$

Khloe should increase each dimension by 11 feet.

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