Answers

1. The sum of the lengths of the other two sides of a right triangle will be 841.

   We have,

   The shortest leg of a right triangle = 29,

   And,

   According to the question,

   The other leg and hypotenuse of a right triangle are consecutive whole numbers,

   i.e.

   Let,

   Other leg = x,

   And,

   Hypotenuse = x+1,

   So,

   Now,

   Using Pythagoras Theorem,

   (Hypotenuse)² = (Perpendicular)² + (Base)²

   i.e.

   H² = P² + B²

   So,

   Now Putting values,

   i.e.

   (x+1)² = x² + 29²

   So,

   On Solving we get,

   x² + 1 + 2x = x² + 841

   ⇒

   x² + 2x – x² = 841 – 1

   We get,

   2x = 840

   So,

   x = 420

   I.e.

   Other leg = 420,

   So,

   Hypotenuse = x+1 = 420 + 1 = 421,

   Now,

   The sum of the lengths of the other two sides of right triangle,

   i.e.

   Hypotenuse + Other leg = 420 + 421 = 841

   Hence we can say that the sum of the lengths of the other two sides of a right triangle will be 841.

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