Mathematics
If the sides of the triangle are in the ratio 3 : 4 : 5, prove that it is right-angled triangle.
Answer
Ratio of sides = 3 : 4 : 5
Let sides be 3x, 4x and 5x cm.
Here, greatest length is 5x cm and other lengths are 3x cm, 4x cm.
Note that (5x)2 = 25x2 and (3x)2 + (4x)2 = 9x2 + 16x2 = 25x2.
Thus, (5x)2 = (3x)2 + (4x)2.
Hence, proved that triangle having sides in the ratio 3 : 4 : 5 is a right-angle triangle.
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