If the length of the hypotenuse of right angled Iscoceles triangle is 12 cm , then the area of the triangle in sqaure centimeters is

Solution

Let Perpendicular be p, base be b and Hypotenuse be h

As it is isosceles right angle triangle, 

so P=B

According to Pythogaras Theorem 

$$h\ =\ \sqrt{\ p^{2\ }+b^2}$$

$$12=\ \sqrt{\ b^{2\ }+b^2}$$

$$12= \ \sqrt{\ 2b^{2\ }}$$

$$12=\ \sqrt{\ 2}\ b$$

$$b\ =\ 6\sqrt{\ 2}$$

Area = $$\ \frac{\ 1}{2}\ \times\ product\ of\ sides\ \times\ \sin\ of\ included\ angle\ $$

       = $$\ \frac{\ 1}{2}\ \times\ b\times\ b\ \times\ \sin\ 90^{\circ\ }$$

       =  $$\ \frac{\ 1}{2}\ \times\ \left(6\sqrt{\ 2}\ \right)^2\times\ 1$$

       = $$\ \frac{\ 1}{2}\ \times\ 72\times\ 1$$

      =36 Answer