Question

The area of a right isosceles triangle whose hypotenuse is 16$\sqrt{2}$ cm is

(a) 125 cm² (b) 158 cm² (c) 128 cm² (d) 144 cm²

Answer 1

Let a be the length of the equal sides of the right isosceles triangle whose hypotenuse is 16$\sqrt{2}$ cm.
Then using Pythagoras theorem in the triangle, we get
a² + a² = (16$\sqrt{2}$)²
2a² = 512
a² = 256
Therefore
Area of the triangle $=\frac{1}{2}\times \mathrm{Base}\times \mathrm{Height}$
$$\begin{gathered} =\frac{1}{2}\times a\times a \\ =\frac{1}{2}\times a^2 \\ =\frac{1}{2}\times 256=128{\mathrm{cm}}^2 \end{gathered}$$
Thus, the area of the square is 128 cm².
Hence, the correct option is (c)