Question

If each side of an equilateral triangle is doubled then find the ratio of the area of the new triangle and the given triangle

Answer 1

Solution :

i ) Let side of an equilateral triangle = a

Area of the triangle = ( √3/4 )a² ---( 1 )

ii ) If side is doubled ,

side of new equilateral triangle = 2a

Area of new triangle = ( √3/4 )× ( 2a )²---( 2 )

iii ) Required ratio = ( 2 )/( 1 )

= [ (√3/4 )×4a² ]/[ (√3/4) a² ]

After cancellation , we get

= 4 : 1

•••••

Answer 2

area of an equilateral triangle=√3/4*a^2

area of an equilateral triangle whose sides are now doubled=√3/4*(2a)^2
=√3/4*4a^2
=√3*a^2

ratio=√3/4*a^2:√3*a^2
=1/4:1
=1:4