Question

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A rectangular garden is fenced on all sides with 98 feet of fencing. The width of garden is 9 feet shorter than it is length. Find the length and width of the garden.

Answer 1

Answer:

Length is 29 feet. Width is 20 feet.

Step-by-step explanation:

We know that the rectangular garden is fenced on all sides with 98 feet of fencing.

In other words, our perimeter is 98 feet.

Remember that the formula for perimeter is:

$P=2(l+w)$

Since we know our perimeter, substitute 98 for P:

$98=2(l+w)$

Now, we also know that our width is 9 feet shorter than our length.

So, whatever our length is, we subtract 9 to acquire the width. In other words:

$w=l-9$

We now have a system of equations. To solve for both w and l, we can use substitution.

Let's substitute our second equation into the first. This yields:

$98=2(l+(l-9))$

First and foremost, let's divide both sides by 2 to simplify. This gives us:

$49=l+(l-9)$

Combine like terms on the right:

$49=2l-9$

Add 9 to both sides. So:

$58=2l$

Divide both sides by 2. Therefore, our length is:

$l=29$

Since our width is 9 feet shorter than our length, our width is 29 - 9 or 20 feet.

So, our length is 29 feet and our width is 20 feet.

And we're done!