Examples: Pythagoras Theorem- 1 Video Lecture | Mathematics for Grade 8

hello friends this video on trangle and
its properties part 18 is brought to you
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so based on whatever we have learned in
the Pythagoras theorem let us quickly
have a look at some of the questions
question number one ABC is a triangle
right angled at C so let us draw a
triangle ABC which is right angled at C
right angled at C means the right angle
is at the vertex C so this is C let us
call this a let us watch this beach this
is ABC a B is equal to 25 centimeters so
AV is 25 centimeters AC is equal to 7
centimeter find the BC so we have to
find out DC so which is the hypotenuse
ad is the hypotenuse so as per
Pythagoras theorem what do we know we
know hypotenuse square is equal to
perpendicular square plus B square so
what is hypotenuse here hypotenuse is 25
so 25 square is equal to 7 square plus B
Square this is something that we need to
find out so 25 square would be 625 7
into 7 would be 49 plus B squared
therefore B Square would be equal to 625
minus 49 which is equal to 576 therefore
B will be equal to root over 576 so root
over 576 means you will have to find out
such a value which when multiplied by
itself gives 576 so how do we find that
so for that we do prime factorization of
576 so how do we do prime factorization
we have learned this in a class 6 right
so you divide it by the smallest
possible prime number so you get numbers
like this and you continue the process
so this is what you get so when you
actually prime factor a is 576 it
out to be 2 into 2 into 2 into 2 into 2
into 3 into 3 so basically this can be
rearranged acted written somewhat like
this you have a total of six three six
twos so three twos together again three
twos together you have two threes so 1 3
& 1 & 3 so what you can do is you this
can be written as 2 into 2 into 2 into 3
so you take one out of these and one out
of this so you get this multiplied by
again the same thing 2 into 2 into 2
into 3 so this is how we do prime
factorization right so 2 2 so for closer
eight threes are 24 so 576 can be
written as 24 into 24 therefore root
over 576 is equal to 24 centimeter
therefore the value of BC would be 24
centimeters question number 2 a 15 meter
long ladder reached a window 12 meters
high from the ground on placing it
against a wall at a distance a so this
is ladder 15 meters height 12 meters and
the distance from the wall is a find the
distance of the foot of the ladder from
the wall so basically we will have to
find the value of a so then we use
Pythagoras theorem so I put in you
square so here which is the hypotenuse
this ladder is the hypotenuse therefore
15 square is equal to 12 squared plus a
squared so 15 into 15 is 225 is equal to
12 into 12 is 144 plus a square or we
can say that a square is equal to 225
minus 144 so this is 81 therefore a is
equal to root over 81 which is equal to
9 centimeters therefore the distance of
the foot of the Lydell from the wall is
9 centimeters question of monthly it
tree it is broken at a height of 5
meters from the ground and its top
touches the ground at a distance of 12
meters from the base of the tree so here
you have to understand some
let's say that you had a three like this
and let's say that this is the ground so
this is how the tree walls initially now
what happened is you and you need to
find the total height of the tree
original height of the tree so this was
the original height of the tree now what
happened was due to some reason this
tree is broken at a height of 5 meters
from the ground so let's say that at a
height of 5 meters from the ground this
tree was broken like this so the tree
was broken and it fell to the ground now
what happened now this is that it has
broken at a distance of 5 meters that
means this height is actually 5 meters
so this height is 5 meters and it also
sees that the top touches the ground at
a distance of 12 meters from the base of
the tree this is the base of the tree
and this is where the top touches the
ground so basically this distance is
given as 12 meters so we have to find
out the original height of the tree so
the original height of the tree would be
this height plus this height right so
you actually need to find this X so once
you find X X plus 5 would be the
original height of the tree so how do we
find X so to find X we make use of
Pythagoras theorem X square is equal to
5 squared plus 12 square so 5 5 so 25 12
into 12 is 144 this is equal to 169 so X
is equal to root over 169 and to root
over 169 is nothing but 13 centimeters
so this is 13 centimeter so original
height would be what this entire height
right so before it was broken that means
when it was not broken this part was
also erect
so basically original height would be
equal to 13
spy that is equal to 18 sending me a few
meters so these are all in meters so the
zeros also meter so the original height
of the tree would be 18 meters thank you
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