Question 602060
{{{ A = 35 }}} in2
{{{ A = (1/2)*b*h }}}
{{{ 35 = (1/2)*b*h }}}
(1) {{{ b*h = 70 }}}
given:
(2) {{{ h = b - 2 }}} in
Substitute this into (1)
(1) {{{ b*( b - 2 ) = 70 }}}
(1) {{{ b^2 - 2b = 70 }}}
Complete the square
(1) {{{ b^2 - 2b + (-2/2)^2 = 70 + (-2/2)^2 }}}
(1) {{{ b^2 - 2b + 1 = 70 + 1 }}}
(1) {{{ ( b - 1 )^2 = 71 }}}
Take the square root of both sides
(1) {{{ b - 1 = sqrt(71) }}}
(1) {{{ b = 1 + sqrt(71) }}} in 
and
(2) {{{ h = b - 2 }}}
(2) {{{ h = -1 + sqrt(71) }}} in
check the answers:
{{{ sqrt(71) = 8.4261 }}}
(1) {{{ b = 1 + 8.4261 }}}
(1) {{{ b = 9.4261 }}}
{2) {{{ h = -1 + 8.4261 }}}
(2) {{{ h = 7.4261 }}}
and
{{{ A = (1/2)*b*h }}}
{{{ A = .5*9.4261*7.4261 }}}
{{{ A = 34.9996 }}}
This looks close enough