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Here is another practical application for using the Pythagorean Theorem.
Imagine you live in a home with a yard shaped like a right triangle.
You really like apples and
would like to plant an orchard around the perimeter,
or the outer edge, of the yard.
The side of the yard that is the hypotenuse of
the triangle is 45 feet long.
A second side of the yard, one of the legs, is 36 feet long.
The length of the third side of the yard is unknown.
When you plant the trees,
each one must be at least 6 feet away from every other tree.
Let us figure out how many trees you can plant around the perimeter.
First we will plug the numbers we know into the theorem.
a squared plus thirty six squared equals forty five squared.
Thirty six squared is one thousand two hundred ninety six.
Forty five squared is two thousand twenty five.
Now we will subtract one thousand two hundred ninety six from
both sides so a squared is by itself on one side of the equation.
a squared equals seven hundred twenty nine.
Take the square root of both sides of
the equation to find the length of side a.
The third side of your yard is twenty seven feet long we are not done yet.
Remember that we are trying to find out
how many trees we can plant along the perimeter,
if each tree must be six feet from every other tree.
To find our answer we need to find the out
the distance around the perimeter of the yard by adding up all three sides.
Twenty seven plus thirty six plus forty five equals one hundred eight.
Divde one hundred eight by the distance between the trees six feet.
You can plant eighteen apple trees around the perimeter of your yard.