The area of an equilateral triangle is proportional to the square of a side. If all of the sides of an equilateral triangle are doubled, what happens to the area?
A)It stays the same.
B)It is doubled.
C)It is tripled.
D)It is quadrupled.

Question

Quizplus · Accepted Answer

Let's use the formula for the area of an equilateral triangle, which is A = (sqrt(3)/4) x s^2, where A is the area and s is the length of a side.

We know that the area is proportional to the square of the side, which means that if we double the side length, the area will be multiplied by (2^2) or 4.

So, if the original equilateral triangle had a side length of s, its area would be A = (sqrt(3)/4) x s^2.

When we double the side length to 2s, the area becomes A' = (sqrt(3)/4) x (2s)^2 = (sqrt(3)/4) x 4s^2 = (sqrt(3)) x s^2.

Comparing the new area (A') to the original area (A), we see that A' is quadrupled (4 times) the size of A. Therefore, the correct answer is D) It is quadrupled.

The Area of an Equilateral Triangle Is Proportional to the Square