The Area of a right angle triangle  is$50c{m}^2$  one of its angle $45°$ . Find the lengths of the sides and hypotenuse of the triangle.

In a right angled triangle if one of the angle is $45°$ , then it is right angle isosceles triangle. Then non-hypotenuse sides are equal.

Let the side be $\text{'}x\text{'}$

Area of triangle $=\frac{1}{2}{x}^2=50{\text{ cm}}^2$

$\Rightarrow x^2=100\Rightarrow x=10$  cm

$AB=AC=10$  then $B{C}^2=A{B}^2+A{C}^2$

$={10}^2+{10}^2$

$B{C}^2=200$

$BC=10\sqrt{2}$