59
100
3
4
(ii) What is the sum of first n natural numbers?
n(n-1)
n(n+1)
(A)
(B)
2
2
(C) on -2) P
)
n(n+2)
2
Answers
Answered by
0
Answer:
) Length of the smallest side is x - d.
Let the length of the other two sides is x, x + d.
Using Pythagoras Theorem,
(x+d)
2
=x
2
+(x−d)
2
x
2
+2xd+d
2
=x
2
+x
2
−2xd+d
2
x
2
=4xd
x=4d
Hence length of the sides is,
x−d=4d−d=3d
x=4d
x+d=4d+d=5d
b) Let x−d,x,x+d be the sides of a right angled triangle in arithmetic progression. Using Pythagoras Theorem,
(x+d)
2
=x
2
+(x−d)
2
x
2
+2xd+d
2
=x
2
+x
2
−2xd+d
2
x
2
=4xd
x=4d
Hence length of the sides is,
x−d=4d−d=3d
x=4d
x+d=4d+d=5d
Hence the sides 3d, 4d, 5d are similar to pythagorean triplet sieds 3, 4, 5.
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