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Permutations And Combinations
If the lengths of the sides of a right angled triangle are in A.P., then show that their ratio is 3 : 4 : 5.
Let a - d, a, a + d, with d>0 be the lengths of sides of a right angled triangle.
∴ a + d, the largest side must be hypotenuse.
So, by pythagorus theorem
or
or or a = 4d
∴ Sides are 4d - d, 4d, 4d + d or 3d, 4d, 5d
Hence, the sides are in the ratio 3:4:5.
Sponsor Area
Determine K, so that K + 2, 4K – 6 and 3K – 2 are three consecutive terms of an A.P.
Sponsor Area