If c is the measure of the hypotenuse of a right triangle, how do you find each missing measure given a=x-47, b=x, c=x+2?

1 Answer
Milena
Feb 8, 2017

a=2+9√57
b=49+9√57
c=51+9√57

Explanation:

a=x−47
b=x
c=x+2

and we know that the pythagoras theorem is:
a2+b2=c2

so if we fill that in:
(x−47)2+x2=(x+2)2

from here we can see that:
a2=x2−94x−2209
b2=x2
c2=x2+4x+4

this leads to:
2x2−94x−2209=x2=4x+4
x62−98x−2216=0

The ABC Formula tells us that in order to calculate x we'll use the following method:

x=−b±√b2−4ac2a
with a=1, b=−98 and c=−2216

when we fill that in we get:
x=98+√−982−(4⋅−2216)2=49+9√57
or
x=98−√−982−(4⋅−2216)2=49−9√57

49−9√57 equals to a negative number, and since we know that x is the length of side b we know that x cannot be negative.
therefore we know that x=49+9√57

we fill that in for the sides:

a=x−47 → a=2+9√57
b=x→b=49+9√57
c=x+2→c=51+9√57

and there's your answer!

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