Question

The sides of a triangle have lengths 5, 7 and x. For what values of x is the triangle a right triangle?.

Answer 1

• The value of x is
  `2√(21) \ or\ 2√(6)`

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The three sides of a right triangle are 5, 7 and x.

Let x be the hypotenuse, then its value as per Pythagorean theorem is:

• 
  `x=√(5^2+7^2)=√(25+49) =√(84) =2√(21)`

Let x be the leg, then the value of x as per Pythagorean theorem is:

• 
  `x=√(7^2-5^2)=√(49-25)=√(24)=2√(6)`