Using the pythagorean theorem how do you find the unknown lengths A=x B=2x-3 C=2x+3?

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Answer 1 · 2016-03-24T05:45:30

#a=24# and #b=45# and #c=51#

From Pythagorean Theorem, we know that
#c^2=a^2+b^2# where a, b are the sides or legs
and c the hypotenuse

From the given,
#c=2x+3#
#a=x#
#b=2x-3#

#c^2=a^2+b^2#
direct substitution

#(2x+3)^2=x^2+(2x-3)^2#

expand the equation

#4x^2+12x+9=x^2+4x^2-12x+9#

simplify

#x^2-24x=0#

solution by factoring

#x(x-24)=0#
the roots are

#x=0# and #x=24#

with #x=0# the sides are #a=0#, #b=-3# and #c=3#
with #x=24# the sides are #a=24#, #b=45# , #c=51#

Check:
#c^2=a^2+b^2#
#51^2=24^2+45^2#
#2601=576+2025#
#2601=2601#
correct !!

God bless...I hope the explanation is useful.