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.