Question 1064987
Let legs and hypotenuse = {{{ a}}}, {{{ b }}}, and {{{ c }}}
(1) {{{ a^2 + b^2 = c^2 }}}
(2) {{{ a + b + c = 2015 }}}
(3) {{{ a/b = 7/11 }}}
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{{{ a }}} would be the shsorter leg
There are 3 equations and 3 unknowns, so it's solvable
(3) {{{ a = ( 7/11 )*b }}}
and
(2) {{{ c = 2015 - a - b }}}
(2) {{{ c = 2015 - ( 7/11 )*b - b }}}
(2) {{{ c = 2015 - ( 18/11 )*b }}}
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{{{ a^2  = ( 7/11 )^2*b^2 }}}
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(1) {{{ ( 49/121 )*b^2 + b^2 = ( 2015 - ( 18/11 )*b )^2 }}}
(1) {{{ ( 170/121 )*b^2 = 4060225 - ( 2*36270/121 )*b  + ( 324/121 )*b^2 }}}
Multiply both sides by {{{ 121 }}}
(1) {{{ 170b^2 = 491287225  - 72540b + 324b^2 }}}
(1) {{{ 154b^2 - 72540b + 491287225 = 0 }}}
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You can use qudratic formula to find {{{ b }}}, then
use (3) to find  {{{ b }}}
Check my math -the numbers are pretty huge !