Using the pythagorean theorem how do you find the unknown lengths A=5x-1 B=x+2 C=5x?

1 Answer
Shwetank Mauria
Feb 13, 2016

Two solutions. The three lengths are either #3, 4 and 5# or #7, 24 and 25#.

Explanation:

It is apparent in three sides of right angled triangle (as Pythagorean theorem is indicated) that among three sides #A=5x-1#, #B=x+2# and #C=5x#, #C# is the largest. Applying Pythagoras theorem,

#(5x-1)^2+(x+2)^2=5x^2# or

#25x^2-10x+1+x^2+4x+4=25x^2# or

#x^2-6x+5=0#. Factorizing this, we get

#(x-5)(x-1)=0# or #x=5 or 1#

Putting #x=5#, the three lengths are #24, 7, 25#

and putting #x=1#, the three lengths are #4, 3, 5#

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