# The hypotenuse of a right triangle is 6m more than the twice of the shortest side.If the third side is 2m less 3m than the hypotenuse.find the side of the triangle.

1
by govindRamesh945
The third side is 2m less than the hypotenuse or 3m ?
if it is clear maybe i can help out in this one
WHICH SIDE
the side other than the hypotenuse and the shortest side. Actually the question is a very little ambiguous.
what does this mean 'the side is two metre less than 3m of the hypotenuse'?

2015-08-21T02:03:44+05:30

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Correction in the question:  The third side is 2 m less than the hypotenuse.

ABC is a right angle triangle at B.    Let AB  <=  BC < AC
AB is the shortest side.

AC = 6 + 2 * AB    meters
BC = AC -  2  meters   = 2 * AB + 4 meters

we know that
AC² =  AB² + BC²
=>  (6 + 2 *AB)²    =  AB² + ( 2 * AB + 4)²
=>  36 + 4 AB²  + 24 AB = AB² + 4 AB² + 16 AB + 16
=>  AB² - 8 AB - 20 = 0
=>    AB = [ 8 +- √[64 + 80]  ] / 2
=>    AB = 10 meters

=> AC = 26 meters      and  BC = 24 meters

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