WEBVTT
00:00:02.660 --> 00:00:10.020
Find the difference between the area of a square whose side length is 17 centimeters and the area of a square whose diagonal length is 20 centimeters.
00:00:11.620 --> 00:00:20.030
So in this problem, what we have are two squares, and what we need to do is work out the area of each of these squares so we can compare them and find the difference between their areas.
00:00:21.390 --> 00:00:26.190
So first of all, to find the area of a square, we know it’s equal to 𝑠 squared, so the side length squared.
00:00:27.650 --> 00:00:29.920
So what we’re gonna do is label our squares A and B.
00:00:31.400 --> 00:00:33.250
So first of all, what we can do is take a look at square A.
00:00:33.250 --> 00:00:35.270
And we know the side length of square A.
00:00:36.700 --> 00:00:45.250
So therefore, we could say that the area of square A is gonna be equal to 17 squared, which is 289 centimeters squared.
00:00:45.280 --> 00:00:45.900
Okay, great!
00:00:45.900 --> 00:00:46.890
So that’s area A.
00:00:48.580 --> 00:00:56.160
So now, if we take a look at our second square, well what we can do is split this into two parts because we’ve got a diagonal and both of these are gonna be right triangles.
00:00:58.000 --> 00:01:03.070
So if we call our side length 𝑠, then what we could do is work out our side length, so therefore, work out our area.
00:01:03.870 --> 00:01:06.470
And to do this, what we’re gonna do is use the Pythagorean theorem.
00:01:08.010 --> 00:01:18.310
And what the Pythagorean theorem states is that 𝑐 squared equals 𝑎 squared plus 𝑏 squared, where 𝑐 is the hypotenuse, so the length of the longest side, and 𝑎 and 𝑏 are the lengths of the shorter sides.
00:01:19.770 --> 00:01:24.500
So therefore, if we take a look at square B, we’re gonna have 20 squared equals 𝑠 squared plus 𝑠 squared.
00:01:24.530 --> 00:01:28.110
And that’s because as it’s a square, both of the shorter sides are the same length.
00:01:29.580 --> 00:01:32.880
So therefore, we can say that 400 is equal to two 𝑠 squared.
00:01:33.690 --> 00:01:36.250
So now, what we could do is divide both sides of the equation by two.
00:01:37.700 --> 00:01:39.990
So when we do that, we get 200 is equal to 𝑠 squared.
00:01:40.430 --> 00:01:44.230
Well now, what we could do is, in fact, take the square root to find out the length of a side.
00:01:44.540 --> 00:01:46.080
However, we don’t need to do this.
00:01:47.750 --> 00:01:49.760
And that’s because we’ve got 𝑠 squared.
00:01:49.760 --> 00:01:54.310
And if we take a look at our formula, we know that the area of the square is gonna be equal to 𝑠 squared.
00:01:56.200 --> 00:02:02.430
So therefore, what we can say is the area of square B is gonna be equal to 200 centimeters squared.
00:02:02.820 --> 00:02:03.400
Okay, great!
00:02:03.400 --> 00:02:07.330
So we now have the area of square A and the area of square B, but have we solved the problem?
00:02:08.960 --> 00:02:11.790
Well, no because what we’re looking to find is the difference between them.
00:02:12.420 --> 00:02:13.570
So let’s find this out now.
00:02:15.460 --> 00:02:24.790
Well, the difference between them is going to be equal to 289 minus 200 because that’s the area of square A minus the area of square B.
00:02:25.930 --> 00:02:27.520
Well, this is gonna give us 89.
00:02:27.710 --> 00:02:38.590
So therefore, we can say that the difference between the area of a square whose side length is 17 centimeters and the area of a square whose diagonal length is 20 centimeters is 89 centimeters squared.