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Q.

A tetrahedron has all its faces triangles with sides 13, 14, 15. The volume of the tetrahedron is  RN,(where R and N are two digited natural numbers) then which of the following is/are CORRECT?

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a

|RN|>30

b

R+N>100

c

R+N<100

d

|RN|<20

answer is A, B.

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Detailed Solution

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a2+b2+c2=152 (14a)2+b2+c2=132 (5a)2+(12b)2+c2=142

Solving the three equations, we get,   a=9,b=92,c=3552 

Volume of tetrahedron  =(16)(14)(12)(3552)=4255

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