Video Transcript
A square has a side length of 𝑙
centimeters and an area of 63 square centimeters. Find the area of a square whose
side length is six 𝑙 centimeters.
Remember, the area of a rectangle
is calculated by multiplying its width by its height. A square is simply a rectangle
whose sides are the same length. And so, we can say that the area of
a square is its side length multiplied by itself or its side length squared. Now, we’re told that our square has
an area of 63 square centimeters. We’re also told that its side
length is 𝑙. So, replacing area with 63 and side
length with 𝑙, we form an equation. We get 63 is equal to 𝑙
squared.
Now, the question wants us to find
the area of a square whose side length is six 𝑙 centimeters. So, what we’re going to do is begin
by calculating the value of 𝑙. In other words, we’re going to
solve this equation for 𝑙. To do so, we perform an inverse
operation. Currently, 𝑙 is being squared. The opposite of squaring is square
rooting a number. This essentially undoes the
previous operation.
And so, if we square both sides of
our equation, we get simply 𝑙 on the right-hand side. Then, the left-hand side is equal
to the square root of 63. Now, it’s worth recalling that when
we find the square root in an equation, we look to find the positive and negative
square roots of the number. But this is a side length, so we
can’t have a negative value. And 𝑙 is equal to the square root
of 63. We might be interested in
simplifying this radical or surd. But in fact, we’re not quite done
with it. So, we’ll leave it as it is for
now.
Our new square has a side length of
six 𝑙 centimeters. We calculated 𝑙 to be equal to the
square root of 63. So, six 𝑙 must be six times
this. It’s six root 63. Since this is the new side length
of our square, the area of this square is this value squared. It’s six root 63 times six root
63. We distribute the two over both
parts of this value. So, we get six squared times the
square root of 63 squared. Six squared is 36.
And of course, squaring and finding
the square root are inverse operations of one another. They undo the other operation. So, the square root of 63 squared
is just 63. This means the area of our square
is 36 times 63, which is 2,268. And since we’re working in
centimeters, the units here are square centimeters.
