SOLUTION: The lengths of the sides of a triangle are 12cm,5cm,13cm.find the length of the perpendicular from opposite vertex to side 13cm long.
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-> SOLUTION: The lengths of the sides of a triangle are 12cm,5cm,13cm.find the length of the perpendicular from opposite vertex to side 13cm long.
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Question 975491: The lengths of the sides of a triangle are 12cm,5cm,13cm.find the length of the perpendicular from opposite vertex to side 13cm long. Found 2 solutions by josgarithmetic, solver91311:Answer by josgarithmetic(39613) (Show Source):
You can put this solution on YOUR website! This is the same kind of question as another one which was recently answered. The method to solve is the same.
Construct your triangle and the desired perpendicular. Note that the intersection of the perpendicular and the side measuring 13cm divides the 13cm side into two segments. Let represent the measure of the shorter segment and then the longer segment must measure . While we are at it, let represent the height we are trying to find. Since the height segment is perpendicular to the 13cm side of the triangle, we have divided the triangle into two right triangles, one with a hypotenuse that measures 5cm and the other with a hypotenuse that measures 12 cm.
We now invoke the magic of Mr. Pythagoras to say:
and
which we can expand to read
Taking the first equation, multiplying by -1, and adding to the second equation gives:
Solving for we get
Calling upon Mr. Pythagoras again we substitute into the first equation to get
After an abundance of arithmetic which I will let you verify for yourself, you get
Which is the desired measurement.
John
My calculator said it, I believe it, that settles it
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