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 $=\frac{1}{2}{x}^2=50{\text{ cm}}^2$

$\begin{array}{l}\Rightarrow x^2=100\Rightarrow x=10cm\\ AB=AC=10thenB{C}^2=A{B}^2+A{C}^2\\ ={10}^2+{10}^2\\ B{C}^2=200\\ BC=10\sqrt{2}\end{array}$