Question

If each side of triangle is doubled,what is the ratio of area of new triangle to that of given triangle

Answer 1

let the each side of the triangle be 'a'
so area will be
A1 = √(3)/2 *a^2. (actually a area of an equilateral triangle)

now if each side is doubled then

A2 = √(3)/2 *(2a)^2
A2 = √(3)/2 *4a^2

now the ratio of new triangle to the original one will be

A2/A1 = [√(3)/2 *4a^2] ÷ [ √(3)/2 *a^2
A2/A1 = 4a^2/a^2
A2/A1 = 4
A2 = 4*A1

hope this helps.
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