the perimeter of a right angled triangle is 60 cm and its area is 120cm². find the lengths of its sides.
Answers
The simplest solution is to assume that the sides are integer length, and test the possibilities,
Assume that it is a 3,4,5 triangle,
Total length = n x 12. n = 60/12 = 5.
Therefore triangle sides are 15,20,25
Area = 15 x 20 / 2 = 150. Not the solution
Assume that it is a 5,12,13 triangle
total length = n x 30. n = 60/30 = 2.
Therefore triangle sides are 10,24,26
Area = 10 x 24 / 2 = 120. Solution found
The triangle sides are 10, 24, 26 cm.
Assume that it is a 3,4,5 triangle,
Total length = n x 12. n = 60/12 = 5.
Therefore triangle sides are 15,20,25
Area = 15 x 20 / 2 = 150.
Not the solution
Assume that it is a 5,12,13 triangle
total length = n x 30. n = 60/30 = 2.
Therefore triangle sides are 10,24,26
Area = 10 x 24 / 2 = 120.
The triangle sides are 10, 24, 26 cm.