Question 136

If the hypotenuse of a right angled isosceles triangle is 8 cm. then its area, in square centimeters, is

Solution

Let the length of equal sides of right angled isosceles triangle = a

In the triangle,

a$$^2$$ + a$$^2$$ = 8$$^2$$

$$\Rightarrow$$ 2a$$^2$$ = 64

$$\Rightarrow$$ a$$^2$$ = 32

$$\Rightarrow$$ a = $$4\sqrt{2}$$ cm

$$\therefore\ $$Area of the right angled isosceles triangle = $$\frac{1}{2}\times a\times a$$

$$=\frac{1}{2}\times4\sqrt{2}\times4\sqrt{2}$$

$$=$$ 16 cm$$^2$$

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