Question 662611


given:

 {{{A=30m^2}}} 


let the base be {{{b}}} and altitude {{{h}}}, 

if the altitude exceeds the base by {{{7m}}}, we have {{{h=b+7m}}}


 {{{A=(1/2)b*h}}} 

 {{{30m^2=(1/2)b*(b+7m)}}} 

{{{30m^2*2=b*(b+7m)}}} 

{{{60m^2=b^2+7bm}}} 

{{{b^2+7bm-60m^2=0}}} ...use quadratic formula to solve for {{{b}}}


{{{b = (-7m +- sqrt(7^2-4*1*(-60m^2) ))/(2*1) }}}


{{{b = (-7m +- sqrt(49+240m^2) ))/2 }}}


{{{b = (-7m +- sqrt(289m^2) ))/2 }}}

{{{b = (-7m +- 17m )/2 }}}...we need only positive root

{{{b = (-7m + 17m )/2 }}}

{{{b = 10m/2 }}}

{{{highlight(b = 5m) }}}


now find {{{h=b+7m}}}

{{{h=5m+7m}}}

{{{highlight(h=12m)}}}