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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