Need help in Aptitude Question

Here it is:

The equivalent resistance, Req, of two resistors R1 and R2, placed in parallel is given by

\(
R_{eq} \: = \: \frac{R_1 \cdot R_2}{R_1 \: + \: R_2}
\)

Show that, if R1 ≤ R2, then

Req ≤ R1

and that

(R1)/2 ≤ Req ≤ (R2)/2

NOTE: I added a lower limit to the last one.

This is a very useful result as it allows you to place bounds on the equivalent resistance of parallel resistors (or inductors, or series capacitors) by inspection. And we've seen how useful bounds can be.
There's an even tighter upper bound: (R1)/2 ≤ Req ≤ (R1+R2)/4
 
Here ya go!:)

The perimeter of a triangle is 67 meters. The longest side is 8 meters longer than the shortest side, and the other side is 5 meters longer than the shortest side. find the length of each side.


Hint -- At ;first blush' this exercise may seem to require certain skills that it does not!:D
 

Thread Starter

RRITESH KAKKAR

Joined Jun 29, 2010
2,829
The perimeter of a triangle is 67 meters. The longest side is 8 meters longer than the shortest side, and the other side is 5 meters longer than the shortest side. find the length of each side.
67=a+b+c
67=x+(x+8)+(x+5)
67=3x+13
67-13=3x
54=3x
a=x=18 the shorter
b=x+8=26
c=x+5=23
 
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