Sequence And Series Question 16
Question: If the sides of a right angled traingle are in A.P., then the sides are proportional to
[Roorkee 1974]
Options:
A) 1: 2: 3
B) 2: 3: 4
C) 3: 4: 5
D) 4: 5: 6
Show Answer
Answer:
Correct Answer: C
Solution:
Let the sides of the triangle be $ a-d,\ a,\ a+d $ , then hypotenuse being the greatest side $ i.e. $ $ a+d $ . So, $ {{(a+d)}^{2}}=a^{2}+{{(a-d)}^{2}} $
$ \Rightarrow $ $ a^{2}+d^{2}+2ad=a^{2}+a^{2}-2ad+d^{2}\Rightarrow a=4d $ Therefore ratio of the side $ s=a-d:a:a+d $ $ =(4d-d)\ :\ 4d:(4d+d)=3:4:5 $ .
BETA
