A right-angled isosceles triangle has an area of 50 square units. Its hypotenuse is (in units):

Correct option is C

Given:

Area of right-angled isosceles triangle = 50 square units

Formula Used:

Area of right-angled isosceles triangle = $$\frac{l^2}{2}$$​​

where, l = length of common sides

Pythagoras Theorem, $$h^2=b^2+p^2$$​​

Solution:

As isosceles triangles have two equal sides, so

​$$50=\frac {l^2}{2}$$​​

​$$l^2=50\times 2 = 100$$​​

​$$l=\sqrt{100}=10$$​ units

Now, if two of the equal sides are 10 units in length.

Then, $$h^2=10^2+10^2=200$$​​

​$$h=\sqrt{200}=10\sqrt2$$​ units