Question 34

A right angled isosceles triangle has hypotenuse of 12 cms. Its area(in sq. cms) is:

Solution

Let the length of the equal side be "a"

$$\Rightarrow$$ a$$^2$$ + a$$^2$$ = Hypotenuse$$^2$$

$$\Rightarrow$$ 2a$$^2$$ = 12$$^2$$

$$\Rightarrow$$ 2a$$^2$$ = 144

$$\Rightarrow$$ a$$^2$$ = 72

$$\therefore\ $$Area of the isoceles right angled triangle = $$\frac{1}{2}$$a$$^2$$ = $$\frac{72}{2}$$ = 36 sq.cms

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