Question 492701: The sides of a triangle are 6cm, 8cm, 10cm. The area of the greatest square that can be inscribed in it, is:
Answer by cleomenius(959)   (Show Source):
You can put this solution on YOUR website! We have a 6 8 10 right triangle.
I set 8 to the y axis and 6 to the x axis.
The equation of the diagonal line, the hypotenuse, will be:
y = -(8/6)x + 8
y = -(4/3)x + 8
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Since this is a square, x = y.
x = -(4/3)x + 8 Now we can solve for x, this will be the length of the side of the square.
Add -(4/3)x to each side.
7/3x = 8
divide each side by 7/3
x = 24/7. This will be the maximum length for the side of square.
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Another formula I came across twice was x*y/x+y.
This checks to the same value, but I could not find a reference to see where it comes from so I did not want to use it, but it is worth keeping in mind.
Cleomenius.
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