Question 143069
Let width = w. Then length = w+50

diagonal = 250
Use Pythagorean theorem.

{{{250^2 = w^2 + (w+50)^2 }}}
{{{62500 = w^2 + w^2 + 100w + 2500}}}
{{{0 = 2w^2 + 100w - 60000}}}
{{{ 0 = w^2 + 50w - 30000}}}

Use quadratic equation and solve. a = 1, b = 50 c = -30000

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}