Question

Find the perimeter of the parallelogram with points at (8,6)(8,18)(13,3)(13,15)

Answer 1

The best way to find the perimeter is to plot the parallelogram so we can see its actual shape and calculate the length of its sides.

Please allow me some time to make a quick plot.

Notice the graph is NOT to proportion, but it will allow us to estimate matematically the length of the four sides.

The easy sides to calculate are the vertical ones, since as you see they extend for exactly 12 units (based on the difference of the y-values for the same value of "x": 15 - 3 = 12 and 18 - 6 = 12.

So we have the length of each of the vertical sides as 12 units.

Now for the "slant" sides, we need to use the formula for the "distance" between any two points on the plane (x1, y1) and (x2, y2) given by the formula:

`d=\sqrt[]{(x2-x1)^2+(y2-y1)^2}`

In our case we have: (x2 - x1) = (13 - 8 ) = 5

and (y2 - y1) = (6 - 3) = 3

Then the bottom slant side becomes:

`d=\sqrt[]{5^2+3^2}=\sqrt[]{25+9}=\sqrt[]{34}`

Notice as well that the distance for the upper slant segment that joins (8, 18) and (13, 15) gives the exact same formula, thus ending in the same quantity:

`d=\sqrt[]{5^2+3^2}=\sqrt[]{25+9}=\sqrt[]{34}`

Finally, the perimeter can be written as:

`P=2\cdot12+2\cdot\sqrt[]{34}\approx35.6619`

Do they ask you to round the answer to any specific number of decimals?

If they don't, you can type it as shown above: 35.6619. If the want the EXACT answer, you need to type it with the specific square root as shown below:

`P=24+2\cdot\sqrt[]{34}`