The length of each side of an equilateral triangle is increased by 20%, resulting in triangle ABC. If the length of each side of the original equilateral is decreased by 20%, resulting in triangle DEF, how much greater is the area of triangle ABC than the area of triangle DEF?

Area of ΔABC is 2.25x the area of ΔDEF.

Step-by-step explanation: Because equilateral triangle has 3 equal sides, area is calculated as

with a as side of the triangle.

Triangle ABC is 20% bigger than the original, which means its side (a₁) measures, compared to the original:

a₁ = 1.2a

Then, its area is

Triangle DEF is 20% smaller than the original, which means its side is:

a₂ = 0.8a

So, area is

Now, comparing areas:

2.25

The area of ΔABC is 2.25x greater than the area of ΔDEF.

answer: 48

just remember to use pemdas:

parentheses

expressions

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addition

subtraction