Problem Of The Week 49
Find the maximum area that can be bound by four line segments of length 1, 2, 3 and 4. (you are not allowed to break a segment, you may join two 🙂 )
1) 6√2
2) 2√6
3) 4√6
4) 3√2
5) None of these
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option e) none of these.
can be triangle or quadrilateral.
if triangle, by hero,s formula max. area is 2sqrt5
and a quadrilateral cannot be formed of the given sides.
qwerty
October 9, 2008 at 8:09 am
what made u think that quad can’t be formed?
outtimed
October 9, 2008 at 8:47 am
We can arrange them in form of a trapezium, with sides 1 and 4 in parallel and two being the perpendicular distance between them…
this gives area as 1/2* 2 * (1+4)=5…max area…correct me???
ankaj
October 9, 2008 at 9:17 am
try again, are you able to make a trapezium?
outtimed
October 9, 2008 at 9:44 am
Yeah..i did a mistake didn’t strike..trapezium is possible buy not with height as 2…it will be less than that…
is the max area=2 sqrt(6)???
ankaj
October 9, 2008 at 10:37 am
yeah , now it is fine
outtimed
October 9, 2008 at 2:31 pm
Explain the answer please…
riya
October 11, 2008 at 5:42 pm
me also got stumped by this questions ..
well we can make quadilateral with sides 4,3,2,1 .. which has max area as root24
trapezium too..
Varun
October 11, 2008 at 11:06 pm
what clicked on my mind is that area is max. if all the vertices lie on a circle. so we can make a cyclic quadrilateral with the given lengths.
and area will come out to be 2*sqrt(6) .
yodha
October 18, 2008 at 5:53 am