You want to make a garden box that has a perimeter of 20.8 feet and a length of 6.3 feet.
What are the exact dimensions of the garden?
The dimensions would be given by the length and the width of the garden, or the rectangle.
This is the garden.
We know the perimeter or distance around the outside is 20.8 feet, and the garden has a
length of 6.3 feet.
This is the length.
We can label this 6.3 feet, as well as the opposite side.
The width is unknown.
Let's represent the width using the variable w.
As long was we know the perimeter would be the sum of the four sides, we can setup in
equation and solve for w.
We can also use the perimeter formula P equals two times L plus two times w to set this up.
Let's go ahead and use the formula.
The perimeter P is equal to two times the length plus two times the width.
The perimeter is 20.8 feet.
So 20.8 equals two times the length of 6.3 feet plus two times the unknown width.
Once we solve the equation for w, we will know the exact dimensions.
Let's first simplify the right side.
Two times 6.3 is 12.6.
We have 20.8 equals 12.6 plus two w.
The next step is to add or subtract to isolate the variable term, which means you want to
undo this positive 12.6 on the same side of the equation as 2w by subtracting 12.6 on
both sides.
Now we simplify.
20.8 minus 12.6 is equal to 8.2.
We have 8.2 equals, this difference is zero, so 8.2 is equal to 2w.
2w means two times w.
Therefore to solve for w, we need to undo this multiplication by dividing both sides
by two.
Simplifying on the right first, two divided by two is equal to one.
One times w is w.
So w is equal to 8.2 divided by 2, which equals 4.1.
Now we know the width is 4.1 feet.
Now we know the garden box is 6.3 feet by 4.1 feet.
Now let's look at a second related question.
Here we are asked to isolate the variable w in the formula for the perimeter of a rectangle,
which means you want to solve this equation for w.
We will do this just like we solved the previous equation for w.
Beginning with the equation P equals two L plus two W.
The first step we isolate the W term by adding or subtracting.
We don't want this positive 2L here.
We subtract 2L on both sides.
On the left side of the equation these are not like terms, so we cannot perform the subtraction.
This is just P minus 2L equals on the right side, 2L minus 2L is equal to zero.
The right side simplifies to 2W.
Now for the next step, we multiply or divide to solve for W. Again 2W means two times W.
Therefore to solve for W, we divide both sides by two.
Simplifying the right first, two divided by two is one.
We have W equals the quantity P minus 2L divided by two.
We an say that W is equal to the quantity P minus 2L divided by 2.
I also want to show how we can write this in a different form.
If we know that W is equal to the quantity P minus 2L divided by 2, we can divide each
term in the numerator by two, which would give us W equals P divided by two minus 2L
divided by two.
Notice in this one, the second fraction simplifies.
W is equal to P divided by two minus L.
We can also express the formula as W equals P divided by two minus L. These two equations
are equivalent, just in a different form.
I hope you found this helpful.