Question

if every side of an equilateral triangle is doubled, then find teh percentage increase in the area of the triangle

Answer 1

Doubling the sides of an equilateral triangle results in a new area which is four times the original area, leading to a 300% increase in area.

Step-by-step explanation:

If every side of an equilateral triangle is doubled, we can find the percentage increase in the area of the triangle by understanding how area scales with the sides of the triangle. The area of an equilateral triangle is given by the formula √3/4 × side2.

Now, if we double the sides, the new area will be √3/4 × (2 × side)2 = √3/4 × 4 × side2, which is four times the original area. Therefore, if the original area is A, the new area is 4A, representing a 300% increase from the original area (since 4A - A = 3A and 3A/A × 100% = 300%).