Question 1104847
Let the width of the rectangle  = {{{ w }}} m
The height of the rectangle is {{{ w + .4 }}} m
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The area of the semicircle = {{{ (1/2)*pi*(w/2)^2 }}} m2
The total area is:
{{{ w*( w + .4 ) + (1/2)*(1/4)*pi*w^2 = 10.4 }}} m2
{{{ w^2 + .4w + ( pi/8 )*w^2 = 10.4 }}} m2
{{{ (( pi + 8 ) / 8 )*w^2 + .4w^2 - 10.4 = 0 }}}
{{{ 1.3927w^2 + .4w - 10.4 = 0 }}}
Rounding off:
{{{ 1.4w^2 + .4w - 10.4 = 0 }}}
Use quadratic formula
{{{ w = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{ a = 1.4 }}}
{{{ b = .4 }}}
{{{ c = -10.4 }}}
{{{ w = (-.4 +- sqrt( .4^2-4*1.4*(-10.4) ))/(2*1.4) }}}
{{{ w = (-.4 +- sqrt( .16 + 58.24 ))/ 2.8 }}}
{{{ w = ( -.4 + sqrt( 58.4 )) / 2.8 }}}
{{{ w = ( -.4 + 7.642 ) / 2.8 }}}
{{{ w = 7.242 / 2.8 }}}
{{{ w = 2.586 }}}
and
{{{ w + .4 = 2.986 }}}
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The height, including semicircle is
{{{ 2.986 + w/2 }}}
{{{ 2.986 + 2.586/2 }}}
{{{ 2.986 + 1.293= 4.279 }}}
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width = 2.586 m
height = 4.279 m
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check:
{{{ 1.4w^2 + .4w  = 10.4 }}}
{{{ 1.4*2.586^2 + .4*2.586 = 10.4 }}}
{{{ 1.4*6.687 + 1.0344 = 10.4 }}}
{{{ 9.3618 +  1.0344 = 10.4 }}}
{{{ 10.3962 = 10.4 }}}
Looks close enough -error due to rounding off