Brad has a garden with dimensions 12 feet long x 7 feet wide. He wants to enlarge the garden to an area of 119 square feet. How much farther will he need to extend the length of the garden to attain his desired area?

Answer 1

To find out how much farther Brad needs to extend the length of his garden to attain an area of 119 square feet, we first calculate the current area of the garden:

The current dimensions are 12 feet long and 7 feet wide.

\[ \text{Current Area} = \text{Length} \times \text{Width} = 12 \text{ ft} \times 7 \text{ ft} = 84 \text{ square feet} \]

Next, we know that he wants to have an area of 119 square feet. The formula for the area of a rectangle is:

\[ \text{Area} = \text{New Length} \times \text{Width} \]

Let \( x \) be the additional length that Brad needs to add to the garden. The new length of the garden will be:

\[ \text{New Length} = 12 \text{ ft} + x \]

The width remains 7 feet. Setting up the equation for the desired area, we have:

\[ (12 + x) \times 7 = 119 \]

Now, we will solve for \( x \):

1. Distributing on the left side:

\[ 84 + 7x = 119 \]

2. Subtracting 84 from both sides:

\[ 7x = 119 - 84 \]

\[ 7x = 35 \]

3. Dividing both sides by 7:

\[ x = \frac{35}{7} = 5 \]

Thus, Brad needs to extend the length of the garden by 5 feet to attain his desired area of 119 square feet. Therefore, the additional length required is:

\[ \boxed{5} \text{ feet} \]