Question

A triangular piece of rubber is stretched equally from all sides, without distorting its shape, such that each side of the enlarged triangle is twice the length of the original side.

The area of the triangle to times the original area.

Answer 1

The area increases to 2 times the original value.

Answer 2

The area of the new enlarged triangle is 4 times the original triangle.

Explanation:

Lets take this triangle to be an equilateral triangle.

Area is given by :
`(√(3) )/(4) * a^(2)`

And let us assume the side to be 7 units.

Area when side is 7 units:

So, area =
`(√(3) )/(4) *(7)^(2)`

= 21.22 square units.

When each side is enlarged to twice. That gives side is 14 units.

So, area =
`(√(3) )/(4) *(14)^(2)`

= 84.87 square units

So, the enlarged area is :
`(84.87)/(21.22)`= 3.999≈ 4 times the original area.

Answer: The area of the new enlarged triangle is 4 times the original triangle.