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# Making a scale drawing

Video transcript

Cole is an urban planner. He wants to create a small
scale drawing of a city block. The block is a square with an
area of 8,100 square meters. Create a scale
drawing of the block using a scale factor of 0.1. So the first thing
we could think about, they give us the
area of the block. And it's a square block. So it has the same
length and width. So we could use that
information to figure out the length and
width of that block. So if it's a square, so let's
imagine a square block right over here. And that this is, I guess we
could call that the length. And then this is also
going to be the length. It's going to be
the same dimensions. We know that the
area is just going to be the length
times the length is going to be equal to 8,100. Or we could say that
our length squared is going to be equal to 8,100. So what times itself
is equal to 8,100? Well, the 81 might
jump out at you. We know that 9 times
9 is equal to 81. But then we have these two
zeroes right over here. But if we give each
of these nines a zero, then we'll end up with
two zeros in the product. So 90 times 90 is
equal to 8,100. So now we know the dimensions
of this square block. It's a 90 meter by 90
meter square block. It's my best attempt
to draw a square block. Now that's the
actual square block. Here let me draw it a little
bit more like a square. My first drawing looked a little
bit too much like a rhombus. So here you go. A little bit better
attempt at a square. Now we want to create at a
scale drawing of the block using a scale factor of 0.1. So the actual block, once again,
is 90 meters by 90 meters. But in our scale
drawing, and I'll do this in this purple
color, we essentially want each of the
dimensions to be 1/10 of their
original dimensions. So we could take
the scale factor and multiply it by each of these
dimensions right over here. So 90 times 0.1, well
that's just going to be 9. This right over here is a 1/10. A 1/10 of 90 meters is
going to be 9 meters. And so this, when we draw the
scale drawing at the scale that Cole intends
to draw it at, we would draw 9 meters by 9 meters. And so let's go
to the actual tool and draw a 9 meter by 9 meter
square, or a 9 by 9 square. We can assume that the units
here are in terms of meters. So let's see. I could draw in that dimension. OK, a 9 there. Let me use my mouse
instead of my pen tool. It'll be easier. And then let me make
this 9, this side 9, and then I could
make this side 9. And then we are all set. It's a square. We see we have
four right angles. And now we can check our answer. And we got it right.