Find the length of its hypotenuse.

Question

The hypotenuse of a right triangle is 13 inches. Its perimeter is 30 inches. Find the length of its hypotenuse.

Answer 1

 Wording is in mistake: Hypotenuse is given 13 inches

  It must be asking to find the lengths of the legs of the triangle

 

legs ( a, b)

 

Hypotenuse ---c

 

 

  a^2 + b^2 = c^2      / Pythagoras theorem

   a + b + c = P          / Perimeter of the triangle

 

    a^2 + b^2 = 13^2 = 169

     a + b = 30 -c = 17

 

      From 2nd equation:

 

        b = 17 -a

 

        Substitute back into 1st equation:

 

       a^2 + ( 17 - a ) ^2 = 169

 

        a^2 + a^2 -34a + 289 = 169

 

         2a^2 - 34a + 120 =0

 

            a^2 - 17a +60 =0

 

             (a - 12) ( a- 5 ) =0

 

            a = 12     a = 5

 

             a = 12,  b = 5  / lengths  of the legs of the triangle.