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

• 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..
  
• 9 years agoHelpfull: Yes(29) No(0)
• 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 .
• 9 years agoHelpfull: Yes(3) No(11)
• 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.
• 9 years agoHelpfull: Yes(1) No(0)
• @vikas jha-why do you take pythagorean triplet???it can be some otheer triangle i.e not a right angle triangle.....
• 9 years agoHelpfull: Yes(1) No(8)
• B) May be even or odd , for different values for different triangles the total area along with square may be odd or even.
• 9 years agoHelpfull: Yes(1) No(0)
• option d even velue
• 9 years agoHelpfull: Yes(1) No(0)
• Can sm1 give me generalized answer ?? I dn want it to be solved by taking examples
• 9 years agoHelpfull: Yes(0) No(0)
• 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.
• 9 years agoHelpfull: Yes(0) No(3)
• D) even only
  
• 8 years agoHelpfull: Yes(0) No(0)
• 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.
• 8 years agoHelpfull: Yes(0) No(0)