Latest Elitmus Aptitude Question SOLUTION: a,b and c are three sides of a right angled triangle . a,b and c are all integers . Area of the triangle is T1. From all three sides a,b and c , we draw a square having areas as S

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(#M40153681) ELITMUS Numerical Ability question Geometry Keep an EYE

a,b and c are three sides of a right angled triangle . a,b and c are all integers . Area of the triangle is T1. From all three sides a,b and c , we draw a square having areas as S1, S2 and S3 . Now, Total area ( T1+S1+S2+S3) is :
A) a fractional value
B) may be even or odd
C) odd only
D) even only

Asked In Elitmus Chetan Anand (8 years ago)

Unsolved Read Solution (10)

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Read Solution (10) :

Vikas Jha  (8 years ago)

D) Even Only
Take any of the pythagorean triplets (3,4,5),(5,12,13),(7,24,25)..e.t.c
I will consider the first one.. a=3,b=4,c=5
then T1= 1/2*3*4= 6(always be even for right angle triangle)
S1= 9(odd)
S2=16(even)
S3=25(odd)
Now T1+S1+S2+S3= 56(even).
also even+even=even, odd+odd=even
Similarly for other cases..

Is this solution Helpfull? Yes (29) | No   

Ajitesh rai  (8 years ago)

I remember the exact option-----

Option A) Can take fractional value

z = 1/2 * (a * b) + a^2 + b^2 + c^2

= T + S1 + S2 + S3

Now , if we take a = 3 and b= 3 , then T = 4.5 is a fractional value , doesnt matter what S1 , S2 , S3 are , overall Z can take fractional value .

Hence , option A) is most appropriate .

Is this solution Helpfull? Yes (3) | No (11)  

chitranshu shrivastava  (8 years ago)

consider 3,4 ,5 sides of a right angle which are the integers and for each side construct a square..........after solving for the area of each one we will get T1=6 , S1=16 , S2=9 and S3=25.............on adding all these values we will get the answer 56 which is an even no.

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swarup  (8 years ago)

@vikas jha-why do you take pythagorean triplet???it can be some otheer triangle i.e not a right angle triangle.....

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Arush Anand  (8 years ago)

B) May be even or odd , for different values for different triangles the total area along with square may be odd or even.

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vamsi krishna  (8 years ago)

option d even velue

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Chetan Anand  (8 years ago)

Can sm1 give me generalized answer ?? I dn want it to be solved by taking examples

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Aayush Shrivastava  (8 years ago)

If we choose, 'a' as base and 'b' as height, and c as hypotenuse, i.e. c= √(a^2+b^2)
and height of triangle = T1 = ab/2
Now, drawing squares from each side, we get areas :
S1 for 'a' : a^2
S2 for 'b' : b^2
S3 for 'c' : c^2, i.e. (√(a^2+b^2))^2 => a^2 + b^2
Now adding all of these,
=> T1 + S1 + S2 + S3
=> ab/2 + a^2 + b^2 +(a^2+b^2)
=> ab/2 + 2( a^2+b^2 )
=> ab/2 + even number ( as a & b are integers)
=> fractional number + even number
=> fractional number
therefore answer is A.

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ashish ranjan  (8 years ago)

D) even only

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Suresh Kumawat  (7 years ago)

if a=base,b=height and c=hypotenuse then c=root(a^2+b^2)
and given that a,b and c are integers so c should be integer
then we have only take pythagorean triplet
so answer
D) Even Only
Take any of the pythagorean triplets (3,4,5),(5,12,13),(7,24,25)..e.t.c
I will consider the first one.. a=3,b=4,c=5
then T1= 1/2*3*4= 6(always be even for right angle triangle)
S1= 9(odd)
S2=16(even)
S3=25(odd)
Now T1+S1+S2+S3= 56(even).
also even+even=even, odd+odd=even
Similarly for other cases.

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