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

Answer:

The area of the enlarged triangle is $4$ times the original area

Step-by-step explanation:

we know that

The scale factor is equal to divide the measurement of the length side of the enlarged triangle by the the measurement of the length of the corresponding side of the original triangle

In his problem

Let

x------> the length side of the original triangle

so

2x----->  is the length of the corresponding side of the enlarged triangle

$scale\ factor=\frac{2x}{x}=2$

$scale\ factor> 1$ -------> that means is increasing

The scale factor squared is equal to the ratio of the area of the enlarged triangle divided by the area of the original triangle

so

Let

m-------> the area of the enlarged triangle

n------> the area of the original triangle

r-------> scale factor

$r^{2} =\frac{m}{n}$

we have

$r=2$

substitute

$2^{2} =\frac{m}{n}$

$m=4n$

therefore

The area of the enlarged triangle is $4$ times the original area