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Question

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


A

19000m2

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B

18225m2

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C

17256m2

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D

18325m2

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Solution

The correct option is B

18225m2


Explanation for the correct option:

Step 1:Finding the base and height of the triangle

Given hypotenuse =270m

Let ABC be a right-angled triangle with hypotenuse AC.

An isosceles triangle has two sides equal.

So AB=BC=a

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

AC2=AB2+BC22702=a2+a272900=2a2a2=729002a2=36,450

Thus, a2=36,450a=36450=190.9188

AB=BC=a=36450=190.9188

Step 2: Finding the area

We know that,

Areaoftriangle=12×base×height=12×AB×BC=12×a×a=a22=364502=18225m2

Thus, the area of the triangle is 18225m2

Hence option B is the correct option.


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