Question 1003494


one side is {{{1/3}}} of the length of the other side:
if longer side is {{{a}}} and shorter side is {{{b}}}, then we have:
 
{{{b=(1/3)a}}}.........eq.1

and if the length of a diagonal is {{{d=9ft}}}, we need to use Pythagorean theorem because two sides of rectangle and its diagonal form right angle triangle

so, we have {{{d^2=a^2+b^2}}}

substitute {{{b}}} from eq.1, and {{{d}}}

{{{(9ft)^2=a^2+((1/3)a)^2}}}........solve for {{{a}}}

{{{81ft^2=a^2+(1/9)a^2}}}

{{{81ft^2=9a^2/9+a^2/9}}}

{{{81ft^2=10a^2/9}}}

{{{81ft^2*9=10a^2}}}

{{{729ft^2=10a^2}}}

{{{729ft^2/10=a^2}}}

{{{72.9ft^2=a^2}}}

{{{a=sqrt(72.9ft^2)}}}

{{{a=8.54ft}}}

then {{{b=(1/3)a=8.54ft/3=2.85ft}}}