Question 1129232

The height of a door is {{{h}}} and the width {{{w}}} 

if {{{h}}} is{{{ 1.3}}} feet longer than its width, we have

{{{h=w+1.3}}} 


and, if its front area is {{{1579.6}}} square feet, we have


{{{h*w=1579.6}}} ...substitute {{{h}}}


{{{(w+1.3)*w=1579.6}}}


{{{w^2+1.3w=1579.6}}}


{{{w^2+1.3w-1579.6=0}}}...... use quadratic formula



{{{w = (-1.3 +- sqrt( 1.3^2-4*1*(-1579.6) ))/(2*1) }}} 


{{{w = (-1.3 +- sqrt( 1.69+6318.4) ))/2 }}} 


{{{w = (-1.3 +- sqrt( 6320.09) )/2 }}} 


{{{w = (-1.3 +- 79.49899370432308)/2 }}} 


we will need only positive solution


{{{w = (-1.3 + 79.49899370432308)/2 }}} 


{{{w = (78.19899370432308))/2 }}} 

{{{w =39.09949685216154}}}->the width of the door


now find {{{h}}}

{{{h=w+1.3}}} 

{{{h=40.39949685216154}}}->the height of the door


these above are {{{exact}}} solutions


if we round to one decimal place we will get:{{{h=40.4}}} and {{{w =39.1}}}

the area will be {{{40.4*39.1=1579.64}}} which is basicaly same; so, you can round it