Question

Sophia is building a rectangular garden and wants to write an equation to represent the perimeter of the garden. The length of the garden is represented by l and the width by w. The perimeter, P, of the garden is calculated by using the formula P=2l+2wIf the perimeter of the garden is 24 feet and the width is 6 feet, what is the length of the garden? Fill in the missing steps to solve the equation. NOTE: Type the numerical values into the blanks to receive credit for this question.(5 points)P=2l+2w=2l+2()24=2l+=2ll= feetSkip to navigation

Answer 1

To find the length $l$ of the garden, we can start with the equation for the perimeter given by:

$$P=2l+2w$$

We know the perimeter $P$ is 24 feet and the width $w$ is 6 feet. Plugging these values into the equation gives us:

$$24=2l+2(6)$$

Now, let's simplify the equation:

$$24=2l+12$$

Next, we need to isolate $2l$. We can do this by subtracting 12 from both sides:

$$24-12=2l$$

This simplifies to:

$$12=2l$$

Now, to find $l$, we divide both sides by 2:

$$l=\frac{12}{2}$$

This gives:

$$l=6\text{ feet}$$

So the length of the garden is 6 feet.