Scale drawings | Geometry | 7th grade | Khan Academy

We're told a scale on a blueprint drawing of a house shows that 10 centimeters represents 2 meters. What number of actual meters are represented by 18 centimeters on the blueprint? So pause this video and see if you can figure it out.

So the main thing to realize is that a blueprint drawing is a scale drawing of something in the real world, in this case of a house. And so what we could do is set up a little bit of a table here. So let's put the drawing on the left, so this is the blueprint drawing, and then this is the real world, real world on the right. And the unit that we're using, the units that we're using in our drawing are centimeters. So we have centimeters over here, and then in the real world we're thinking in terms of meters.

And so let me make a little bit of a table. And so we see that 10 centimeters on the drawing corresponds to 2 meters in the real world. So 10 centimeters in the drawing corresponds to 2 meters in the real world. Then they ask us what number of actual meters are represented by 18 centimeters on the blueprint. So 18 centimeters on the blueprint would correspond to what in the real world?

Well, there's several ways to approach it. One way to think about it is: look, to go from 10 to 18, we are going to multiply by 1.8. So to go from what 10 centimeters represents in the real world to what 18 centimeters represents in the real world, you would similarly multiply by 1.8. So times 1.8, which would give us 3.6. 3.6, what? 3.6 meters in the real world. So 3.6 meters in the real world would be what 18 centimeters on the blueprint represents.

Let's do another example. Jalen draws a hen with a scale of two units on her graph paper, representing six meters, six centimeters in the real world. The hen is 16 units tall in the drawing. What is the height in centimeters of the actual hen?

So once again, pause this video and see if you can figure that out. All right, so let's just set up our tables again. So our table, so we have our drawing and then we have the real world. In our drawing, it's just these little units on our graph paper, so I'll call just that units, and the real world we're thinking in terms of centimeters.

And so let me set up a little bit of a table here. And so we know and we see that right over here from this scale, we can see that two units represent six centimeters in the real world. So two units in our drawing represent six centimeters in the real world.

And then they say the hen is 16 units tall in the drawing. So it's 16 units tall in the drawing. What would that represent in the real world, which would be the actual height of the hen if two units represent six centimeters? And now we have eight times as many units. Well, that's going to represent eight times as many centimeters.

So, six times eight is 48 centimeters. So what is the height in centimeters of the actual hen? 48 centimeters. 48, and we're done.