Question 776883
Let the length be L ft and diagonal be D ft.


Using Pythagoras theorem
{{{Diagonal^2 = Length^2 + Width^2}}}
{{{D^2 = L^2 + 50^2}}} _______ (1)


Also, {{{D = L + 10}}}


Substituting for D in terms of L in (1)
{{{(L + 10)^2 = L^2 + 50^2}}}
{{{L^2 + 20L + 100 = L^2 + 2500}}}
{{{20L = 2400}}}
{{{L = 2400/20 = 120}}}


The length is 120 ft.