Question 1078427

A right triangle has a hypotenuse that is 3 feet longer than one leg. The other leg is 4 feet

let's a hypotenuse be {{{c}}}, one leg {{{a}}}, and other leg {{{b}}}

if  a hypotenuse that is {{{3}}} feet longer than one leg, we know that {{{c=a+3}}}
and, if the other leg is {{{4}}} feet, we know that {{{b=4}}}

use Pythagorean theorem:

{{{c^2=a^2+b^2}}}.....substitute {{{c=a+3}}} and {{{b=4}}}

{{{(a+3)^2=a^2+4^2}}}....solve for {{{a}}}

{{{a^2+6a+9=a^2+4^2}}}

{{{a^2+6a+9-a^2=16}}}

{{{6a=16-9}}}

{{{6a=7}}}

{{{a=7/6}}}


then {{{c=a+3}}}=>{{{c=7/6+18/6}}}=>{{{c=25/6}}}