To find out how much farther David needs to extend the length of the garden to achieve an area of 126 square feet, we start by calculating the existing area of his garden.
The current dimensions of the garden are:
- Length = 11 feet
- Width = 9 feet
The area \( A \) of the garden is calculated as: \[ A = \text{length} \times \text{width} = 11 \text{ ft} \times 9 \text{ ft} = 99 \text{ ft}^2 \]
Now, he wants to enlarge the garden to an area of 126 square feet. We can let \( x \) be the additional length he needs to add to the existing length. The new length will be \( 11 + x \) feet, and the width remains 9 feet.
The equation for the desired area becomes: \[ (11 + x) \times 9 = 126 \]
We can simplify this equation: \[ 99 + 9x = 126 \]
Now, we subtract 99 from both sides: \[ 9x = 126 - 99 \] \[ 9x = 27 \]
Next, we divide both sides by 9: \[ x = \frac{27}{9} = 3 \]
Thus, David needs to extend the length of the garden by \( \boxed{3} \) feet to attain the desired area of 126 square feet.
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