Welcome to "A Rectangle Has an Area of 345 sq ft and a Width of 15 ft — What’s the Length?" with Mr. J! Need help with finding the missing side of a rectangle given the area? You're in the right place!
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Welcome to Math with Mr. J.
In this video, we're going to answer the question,
a rectangle has an area of 345 square feet and a width of 15 feet.
What is the length of the rectangle?
Well, we're going to solve this using algebra,
and we know that the area of a rectangle equals length times width.
So area equals length times width.
And I'm using a cursive l there just so we don't confuse a lowercase l with a 1.
And then I'm using a dot for the multiplication sign instead of an x.
That's because we're going to be using algebra here.
And x is a very common variable in algebra,
so we don't want our multiplication sign mistaken for a variable.
So this is just a different way of writing out multiplication.
We're not changing anything here.
Now what we need to do is use what we know,
so what we are given, to figure out what we don't know.
That's going to be the length of the rectangle.
So we're going to plug in what we are given, the area and the width.
So the area is 345 square feet.
So let's plug in 345 for the area.
Equals the length, which is our unknown, so keep our l there,
times the width, which is 15 feet.
So plug in 15 for the width.
So our unknown length times 15 needs to equal 345.
So what number times 15 equals 345?
If we have numbers that we can figure out using mental math, go ahead and do so.
But here we're going to go through this and figure this out by solving this one-step equation,
because I'm not sure what number times 15 will give us that area of 345.
So we need to work this out.
And remember, when solving equations, we want to isolate the variable.
Get the variable on one side of the equation by itself.
That's the l here.
l is being multiplied by 15, so we need the inverse operation.
The opposite operation in order to isolate l.
What's the opposite of multiplication?
Well, division.
So we need to divide the right side of the equation by 15.
Remember, whatever we do to one side of an equation, we must do to the other.
So divide the left side by 15 as well.
The 15s on the right side of the equation cancel each other out, so l is now isolated,
equals, and then on the left side of the equation, we have 345 divided by 15.
So we need to figure that out.
Let's divide by hand over to the side here.
So 345 divided by 15.
So we'll start with 3 divided by 15, which we can't do.
So we move over to the 4, and we have 34 divided by 15.
So how many whole groups of 15 in 34?
How many 15s in 34?
Well, 2.
That gets us to 30.
So we put the 2 above the 4.
And make sure that 2 is above the 4, not the 3, since we did 34 divided by 15.
Now we multiply.
2 times 15 is 30.
Subtract.
34 minus 30 is 4.
Bring down the 5.
And now we have 45 divided by 15.
That's 3.
We hit 45 exactly here.
3 times 15 is 45.
Subtract.
45 minus 45 gives us 0.
So we end up with 23.
L equals 23, or the length equals 23.
And that's our answer.
And we can even write this out as the length equals 23 feet.
And that's going to be choice A.
So there you have it.
There's the answer to our question.
If you need more examples or help with this, check the description for a follow-up video.
So whether you're studying for a test, learning this in class,
or maybe you were just looking for a problem to solve.
Whatever the case may be, I hope that helped.
Thanks so much for watching.
Until next time, peace.
