Question 1022855
Let {{{ a }}} = the length in meters of
the shorter leg
Let {{{ b }}} = the length in meters of 
the longer leg
Let {{{ c }}} = the length in meters of
the hypotenuse
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(1) {{{ c^2 = a^2 + b^2 }}}
(2) {{{ c = a + 5 }}}
(3) {{{ c = b + 2 }}}
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(2) {{{ a = c - 5 }}}
and
(3) {{{ b = c - 2 }}}
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Plug (2) and (3) into (1)
(1) {{{ c^2 = ( c - 5 )^2 + ( c - 2 )^2 }}}
(1) {{{ c^2 = c^2 - 10c + 25 + c^2 - 4c + 4 }}}
(1) {{{ c^2 = 2c^2 - 14c + 29 }}}
(1) {{{ c^2 - 14c + 29 = 0 }}}
Complete the square:
(1) {{{ c^2 - 14c + ( 14/2 )^2  =  -29 + (14/2 )^2 }}}
(1) {{{ c^2 - 14c + 49 = -29 + 49 }}}
(1) {{{ c^2 - 14c + 49 = 20 }}}
(1) {{{ ( c - 7 )^2 = 20 }}}
Take the square root of both sides
( note that I don't use the negative square root
since that gives me a negative result for {{{ a }}} )

(1) {{{ c - 7 = sqrt(20) }}}
(1) {{{ c = 4.472+ 7 }}}
(1) {{{ c = 11.472 }}}
and
(2) {{{ a = c - 5 }}}
(2) {{{ a = 11.472 - 5 }}}
(2) {{{ a = 6.472 }}}
and
(3) {{{ b = c - 2 }}}
(3) {{{ b = 11.472 - 2 }}}
(3) {{{ b = 9.472 }}}
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The perimeter is:
{{{ 11.472 + 6.472 + 9.472 = 27.416 }}}
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check:
(1) {{{ c^2 = a^2 + b^2 }}}
(1 ) {{{ 11.472^2  = 6.472^2 + 9.472^2 }}}
(1) {{{ 131.607 = 41.887 + 89.719 }}}
(1) {{{ 131.607 = 131.606 }}}
error due to rounding off
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