Question 1084356
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<pre>
Let x be the length of either leg (the legs are congruent, since the triangle is isosceles).


Then the area of this right-angled triangle is {{{(1/2)*x*x}}} = 5000 m^2, which implies

{{{x^2}}} = 10000 m^2, i.e.   x = 100 m.


Then the hypotenuse is {{{100*sqrt(2)}}} and the perimeter is {{{200+ 100*sqrt(2)}}} m.
</pre>

Solved.



Notice that "josgarithmetic" mistakenly uses the term "diagonal", which is not applicable in this case.