Question 59264
For this you need the Pythagorean Theorum.
{{{ a^2 + b^2 = c^2 }}}
a = length (altitude) = b+50
b = width (base) = b 
c - diagonal (hypotenuse) = 250
{{{ a^2 + b^2 = c^2 }}}
{{{ (b+50)^2 + b^2 = 250^2 }}}
Foil the binomial
{{{ b^2 + 100b + 2500 + b^2 = 250^2 }}}
combine like terms
{{{ 2b^2 + 100b + 2500 = 250^2 }}}
Square the Hypotenuse
{{{ 2b^2 + 100b + 2500 = 62500 }}}
Move all values to the left side
{{{ 2b^2 + 100b + 60000 = 0 }}}
Divide all parts by 2
{{{ b^2 + 50b - 30000 = 0 }}}
Factor
{{{ (b+200)(b-150) = 0 }}}
set each piece equal to 0
{{{ (b+200)=0}}} and {{{(b-150) = 0 }}}
{{{ b = -200 }}} and {{{ b = 150 }}}
a Distance CAN NOT be a negative value.
{{{ b = 150 }}}


Substitute
{{{ a = b + 50 }}}
{{{ a = 150 + 50 }}}
{{{ a = 200 }}}


Dimentions:
Length = 200
Width = 150