Problem Set on Square : 2 - Geometry of Quadrilaterals, Quantitative Aptitude Video Lecture | Study UPSC Prelims Paper 2 CSAT - Quant, Verbal & Decision Making - UPSC | Best Video for UPSC

a park square in shape has a three meter
wide Road inside running along its sides
the area occupied by the road is 1764
square meters what is the perimeter
along the outer edge of the road so you
have a situation like this the area
enclosed by this red square is the park
and the shaded region is the road which
is of three meters wide and it is
running along the sides of this park and
you have been given the area of the
shaded region and that's 1764 meter
square now you have been asked what is
the parameter along the outer edge of
the road that means the perimeter of
this red square ok so let us assume that
the side of inner square is s so the
side of the outer square will be s plus
6 isn't it we have three meters on both
the sides so this will be s plus 6 ok
now the area of the outer square minus
the area of the inner square will give
you this area of the shaded region so I
have s plus 6 volt square minus s square
will be equals to 1764 ok let us solve
this s square plus 2 times s times 6
that's 12 s plus 6 square that's 36
minus s square is equals to 1764 this s
square and this egg s square gets
cancelled out what remains is 12 s is
equals to 1 7 64 minus 36 so 12 s is
equal to 1728 so s is equal to 1728 / 12
and that is equals to 144 so this is the
side of this inner square side of the
outer square will be 144 plus 6 and
that's 150 so 150 is the side of the
outer square and you need the perimeter
of the outer square so perimeter is
equal to four times the side of a square
so this is 4 times 1 50 and that is 600
meters so we have the answer as option
be a man walked diagonally across a
square lot approximately what was the
percentage saved by not walking along
the edges so this is the diagrammatic
representation of our question we have a
square lot and a man starts from here
right and he goes diagonally across now
if this man had to travel along the
edges he would have traveled like this
okay now let us assume that if this man
walks along the edges he walks let's say
100 kilometers so the distance traveled
along the edges we have assumed as 100
units okay so as this complete distances
hundred units the half of it will be 50
units so the man travels 50 units
horizontally and 50 units vertically now
let us calculate how much distance he
travels when he walks diagonally like
this px now as this is a square this
will be a right-angled triangle this one
so we can apply pythagoras theorem so we
have x square is equal to 50 square plus
50 square so therefore x square is
equals to 2500 plus 2500 and that will
be equals to x square is equals to 25
plus 25 is 50 and this 100 so 5,000 so
therefore x is equal to under root of
5,000 and this will be equals to 70
point 71 if you solve it now you can
right 70-point 71 as approximately 70
okay now you have been asked what was
the percentage saved now we can call it
percentage because we took the base
value as hundred now what was the
percentage saved to calculate that we
will have to subtract 70 from 100 so 100
minus 70 and that is equal to thirty
percent was saved okay if had he
traveled along the edges he would have
traveled hundred kilometers but he
traveled diagonally so he travelled only
70 kilometers so he saved 30 kilometers
so in our context he saved thirty
percent so option C is the correct
answer the area of a square field is 60
9696 square centimeter what is the
length of its diagonal so this is your
square let us say that it has side s
what will be the length of the diagonal
well this being a right angle triangle
you can apply pythagoras theorem so s
square plus s square taken under root so
the diagonal will be under root of s
square plus s square and that's root 2 s
square right so in other words i can say
root 2 s as the diagonal now you have
been given the area area is equals to
side square so side square is equals to
6 96 96 right you have the value of s
square diagonal is equal to root 2 s
square right so this will be root of two
into six 96 96 right so you can split
this up root 2 times the route 69 696 so
this is equal to under root 2 is 1.4 14
times if you calculate the under root of
six 96 96 you will get it as 260
for right so 1.4 14 x 264 and that is
373 point two nine six if you calculate
and this will be in centimeters okay so
the length of the diagonal we have found
out option C is the correct answer if
the ratio of areas of two squares is 225
is to 256 then what is the ratio of
their perimeters well you have been
given the ratio of the areas so i can
write a1 by a2 is equals to 225 x 256
now what is the formula for the area of
a square and that is side square so i
can write s 1 square by s 2 square is
equals to 225 x 256 taking under root on
both the sides i get this okay now under
root of s 1 square is s 1 under root of
s 2 square is s 2 so s 1 by s 2 is equal
to root 2 25 that's 15 upon root 256
that's 16 this is one thing we have
found out now we have been asked what is
the ratio of the parameters so p1 by p2
what is the formula for the perimeter of
a square that is four times the side so
for p1 we have four times s 1 upon 4 p-2
we have four times s 2 so this gets
cancelled out this is basically s 1 by s
2 and that is 15 x 16 so the ratio is 15
is 260 isn't it so option c is the
correct answer