Question 923629: If there is a triangle which has sides of 60, 80 and 100 for lengths and you split the triangle so that it creates 2 right triangles (separating the triangle on the 100 length side) what would be the lengths of the 4 new sides which have been created?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you will have 2 triangles.
the first triangle will have sides of 36, 48, 60
the second triangle will have sides of 64, 48, 80
you drop a perpendicular from the vertex of the angle opposite the 100 length side and perpendicular to it.
your 100 length is split into 2 pieces.
one piece is x units in length.
the other piece is 100 - x units in length.
your altitude has a length of z units.
since you have 2 right triangles with a common altitude, you can set up an equation using the pythagorean formula as follows:
x^2 + z^2 = 60^2 for the first triangle.
(100-x)^2 + z^2 = 80^2 for the second triangle.
solve both of these equations for z^2 and you get:
z^2 = 60^2 - x^2 and z^2 = 80^2 - (100 - x)^2
since both expressions on the right sides of these equations are equal to z^2, you can set them equal to each other to get:
60^2 - x^2 = 80^2 - (100 - x)^2
solve this equation for x and you get x = 36.
that makes 100 - x = 64.
you can use either equation to solve for z and you will get z = 48.
for example:
z^2 = 60^2 - x^2 becomes z^2 = 60^2 - 36^2 which makes z^2 = 2304 which makes z = 48.
solve for z^2 in the other equation and you will get the same answer.
z will be equal to 48 in that other equation as well.
confirm your solutions by using the pythagorean formula on each triangle and you will see that the values given for x and 100-x and z are good in both triangles.
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