Given a triangle ABC
Column A
perimeter of the triangle ABC.
Column B
Twice the perimeter of a similar triangle whose area is half the area of triangle ABC.
A) if the quantity in column A is greater.
B) if the quantity in column B is greater.
C) if the quantities are equal.
D) if the relationship cannot be determined from the information given.
(Asked by Vivek)
i suppose its B).
i think c)option
plz tell and explain the answer
We can find exact value by putting any numeric value.
consider a equilateral triangle (for simplicity) of side ‘a’ units(let)
=> perimeter=3a
area=(3^0.5/4)a^2=A1(let)
another equialteral similar triangle with half area cn be written as…
b=each side(let)
area=A2=(3^0.5/4)b^2
A2=A1/2
=>each side=b=a/2^0.5 (clearly by comparing two areas)
hence twice the new peri will be ’6b’
now new peri.=6b=3*1.414a
obviously 6b>3a..hence option B.
Avinash.. why you have not taken a numeric ?? I think that would be more easier.
hmmm yess but thts for those who wanted a more convincing explanation…
ya puttin in values is lot simpler..thts the way gre shuld be solved i gess…hehe neva thot of it..
Avinash,
I know it is education system/pattern where we always think in term of algebra.
Ok great going..
consider a right traingle with same sides a
then the similar triangle with half the area has a side of a/sqrt2
in that case perimeter of the triangle with the side a is naturally more!!!
“”"consider a right traingle with same sides a”"
— Is that possible ?
Sorry Karthik can you explain ?
d.u cant determine.perimeter can be sum of a,2a ,3a, 4a[becoz while finding area u need to know the base and height.base can be anything a,2a,3a etc].U dnt knw which side to take and no whr it has been stated thet its an equilateral triangle
B
B
since all corresponding sides of two similar triangles are in same ratio and its given that the areas are in ratio 1:2 the sides ratio naturally would be 1:sqrt(2) from that the perimeter ratio would be 1:sqrt(2) but on multiplying by 2 the ratio wud be reversed to sqrt(2):1 so Column B would be greater
ans?
b or c