Q3 of 99 Page 258

The length of hypotenuse of an isosceles right - angled triangle is 12√2 cm. Let us write by calculating what will be the area of that field.

Given


In an isosceles right angled triangle


Hypotenuse = 12√2 cm


Since it is the isosceles triangle


⇒ the length of the remaining two sides would be same


Let the length of remaining two sides be x cm


According to the Pythagoras theorem,


Hypothenuse2 = Base2 + height2


⇒ (12√2)2 = x2 + x2


⇒ 144 × 2 = 2x2


⇒


⇒ 144 = x2


⇒ x = ± 12 cm


Since length cannot be negative


⇒ Length (x) of remaining two sides = 12cm


Area of an isosceles triangle



= 72cm2


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