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Find the length of its hypotenuse.

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1 Answer

 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.