How do you use the Pythagorean theorem to find the missing side a given c=13, b=6a?

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Answer 1 · 2017-02-10T12:35:05

See the entire solution process below:

The Pythagorean Theorem states, for a right triangle:

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

Substituting and solving using the values given in the problem for #b# and #c# results in:

#a^2 + (6a)^2 = 13^2#

#a^2 + 36a^2 = 169#

#1a^2 + 36a^2 = 169#

#(1 + 36)a^2 = 169#

#37a^2 = 169#

#(37a^2)/color(red)(37) = 169/color(red)(37)#

#(color(red)(cancel(color(black)(37)))a^2)/cancel(color(red)(37)) = 4.568#

#a^2 = 4.568# rounded to the nearest thousandth.

#sqrt(a^2) = sqrt(4.568)#

#a = sqrt(4.568) = 2.137# rounded to the nearest thousandth.