How to Find the Perimeter Using the Distance Formula

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Finding the perimeter using the distance formula only requires you to know the lengths of each side of the shape. Find the perimeter using the distance formula with help from an experienced mathematics professional in this free video clip.

Part of the Video Series: Math Calculations
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Hi, I'm Drew Moyer, and this is how to find perimeter using the distance formula. To find the perimeter we are going to need to use the distance formula to find the lengths of each of the sides of the shape that we are trying to solve for and here we have our shape. It's a triangle so we're going to need to use the distance formula three separate times. So the distance formula is just like this D equals the square root of X2 minus X1 squared plus Y2 minus Y1 squared and to use it all we have to do is plug in the coordinates that we already know. So I'm going to do side A first which you can see is between these two points. So I'm going to plug in negative 2 for this X value, negative 2 minus the X value over here which is 2 squared plus my Y value over here which is negative 1 minus my Y value over here which is 3 and then we just solve. D sub A equals negative 2 minus 2 which is 4 squared plus negative 1 minus 3 which is negative 4 squared. So D sub A equals minus 4 squared which is 16 plus minus 4 squared again, 16 which is the square root of 32 which I can then simplify by pulling out the square root of 16. So I get D sub A equals 4 root 2. And for the next two it's a very similar process. So I'm going to do D sub B equals square root of X2 minus X1 squared plus Y2 minus Y1 squared. And then I just plug in my coordinates for B which you can see I have a 2 minus my X value down here which is 3, 2 minus 3 squared plus Y2 which is 3 and my Y1 which is negative 4. So 3 minus negative 4 squared and then again just simplify, D sub B equals 2 minus 3 which is negative 1 squared plus 3 minus negative 4 which turns into 3 plus 4, 7 squared, D sub B equals negative 1 squared which is 1, 7 squared is 49 and I have D sub B equals root 50 which I can then simplify by pulling out a square root of 25 which is 5 and I'm left with a root 2, so 5 root 2 and then the third process is again very similar, D sub C equals X2 minus X1 squared plus Y2 minus Y1 squared and I'm plugging in for side C which I have a minus 2 minus 3 squared and over here for Y I've got a minus 1 and minus negative 4 squared. D sub C equals minus 2 minus 3 which is a minus 5 squared plus negative 1 minus negative 4 which would be plus 4 so 3 squared. D sub C equals negative 5 squared is 25, 3 squared is 9, D sub C equals 25 plus 9 which is 34. So now to use the perimeter all I have to do is add up each of these three and I've got 5, root 2 plus 4 root 2 plus root 34 and I can simplify these to get 9 root 2 plus root 34. So there it is. Again, I'm Drew Moyer, and this is how to find perimeter using the distance formula.

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