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Q.

Find the side of an isosceles right-angle triangle with an area of 500 sq.cm.


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a

     10 m

b

     10 cm

c

     100 cm

d

     50 m 

answer is B.

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Detailed Solution

An isosceles triangle has two equal sides. In an isosceles right triangle, since the hypotenuse is the longest side, the two equal sides are the base and height of the triangle.
Let a be the base and height of the triangle.
Area of a right angle triangle is given by
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" width="87" height="91" alt=a=10 cm
Hence, Option (2) is the correct answer.
  
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