Question 198854
Start with the formula for the area of a triangle:
{{{A = (1/2)b*h}}} In an isosceles triangle, as in this problem, the b and h are equal, let's call them x, and the area is given as 50sq.cm., so...
{{{50 = (1/2)(x*x)}}} Multiply both sides by 2.
{{{100 = x^2}}} Take the square root of both sides.
{{{x = 10}}}
Each of the legs is 10 cm.
The hypotenuse (c) can be found by the Pythagorean theorem:{{{c^2 = a^2+b^2}}}, where a = 10cm. and b = 10cm.
{{{c^2 = 10^2+10^2}}}
{{{c^2 = 100+100}}}
{{{c^2 = 200}}} Take the square root of both sides.
{{{c = sqrt(200)}}}
{{{c = 14.14}}}cm.  Approx.