The area of a right-angled isosceles triangle whose hypotenuse is equal to 270 m is :

(A) 19000 m2

(B) 18225 m2

(C) 17256 m

(D) 18325 m2

Solution:

Given hypotenuse = 270 m

Let ABC be a triangle with hypotenuse AC.

An isosceles triangle has 2 sides equal.

So AB = BC = a

Since triangle is right-angled isosceles triangle, we use Pythagoras theorem

AC2 = a2 + a2

=> 2 a2 = 2702

=> a2 = 2702/2

Area of triangle ABC = ½ (base×height)

= ½ a2

= 2702/4

= 18225 m2

Hence option B is the answer.

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