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How many right triangles whose sides are all positive whole numbers having the property that the area is numerically equal to the perimeter?

How many right triangles whose sides are all positive whole numbers having the property  that the area is numerically equal to the perimeter?

Grade:12th

1 Answers

Aman Bansal
592 Points
11 years ago

Dear Abhishek,

: Let the triangle have leg lengths a and b, with a, b are whole numbers.

The given condition implies that

1/2ab = a + b +(a2 + b2)^1/2

Thus solving this to get the set of  possible values of a,b 

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