Mathematics

Question

Length and area of right triangle
Length and area of right triangle

1 Answer

  • Answers:
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    a)   The length
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         The length of the hypotenuse is:  "(mn√61)" .

         The lengths of each of the 3 (THREE) sides are:  5m, 6n, (mn√61).
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    b)   The area of the triangle:   "15mn  square units " ; 
                                or, write as:  " 15mn units²  ".
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    Explanation:
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    Area of triangle = (½) * (base) * (height);  that is:

                A = (½ ) * b * h
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             Substitute our known values from the image attached; and plug in these values; to find the area:
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    A =  (½ ) * (5m) * (6n) =
    ↔  
          A = (½) * (6n) * (5m) =

         3n * 5m = " 15mn square units " ;or, write as:  "15mn units² " .
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    Length:  This is a right triangle: 
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    So:  a² + b² = c² ;
      in which "c" is the length of the "hypotenuse"; 
                    "a" = the length of one of the other sides ;
                    "b" = the length of one of the other sides (not used for "a").
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       Given: a = 5m ; b = 6n ;  Solve for "c"  (the hypotenuse).

       c² = a² + b²  ;

       c² = (5m)² + (6n)² ;

       c² = (5m)(5m)  + (6n)(6n) ;

       c² =  25m²  + 36n² ;

       c = +√(25m²  + 36n²) ;

       c = mn * √(25 + 36)  ;

       c = mn √61
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    So, the length of the hypotenuse is:  "mn√61"

    The lengths of each of the 3 (THREE) sides are:  5m, 6n, (mn√61).
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