Question

A triangular piece of rubber is stretched equally on all three sides (without distorting or changing its shape) such that the new sides are 2 times the length of the original sides. How does the area of the triangle change?

A. The area increases to 2 times the original value.
B. The area increases to 4 times the original value.
C. The area increases to 6 times the original value.
D. The area increases to 8 times the original value.

Answer 1

Hints:
Here the scale factor is 2 because new sides are 2 times the lengths of the original sides.

Length of each side is measured in metres, so linear dimensions (lengths) vary with scale factor.
Area is measured in metre\(^2\), so areas vary with scale factor\(^2\).
Volume is measured in metre\(^3\), so volumes vary with scale factor\(^3\).

Answer 2

Oooh
Okay thank you. I gtg now but thank you a ton

Answer 3

area of triangle with base length b and height a:

\[A=\frac{ab}{2}\]

now let's call the new area the stretched area A prime with a little mark on it like this A'. That means we doubled the lengths:
\[A' = \frac{(2*a)(2*b)}{2} = 4\frac{ab}{2}=4A\]
Maybe complicated, but what I showed is that the stretched area A' is equal to four times the old area A. Think about it a bit, it's pretty powerful stuff.