Question

Triangle ABC and triangle DEF are equilateral triangles, A(triangle ABC): A(triangle DEF)=1:2. If AB=4 then what is length of DE?

Answer 1

4√2 units

Explanation:

• If two triangles are equilateral, their areas are directly proportional to the squares of their side lengths.

• In this case, you're given that the ratio of the areas of triangle ABC to triangle DEF is 1:2.
• Since the ratio of the areas is equal to the ratio of the squares of their sides, you can write:

(Area of triangle ABC) / (Area of triangle DEF) = (AB)² / (DE)²

Given that AB = 4 and the ratio of areas is 1:2, you can set up the equation as follows:

1/2 = 4² / (DE)²

Now, solve for DE:

DE² = 4² / (1/2)

DE² = 4² × 2

DE² = 16 × 2

DE² = 32

Taking the square root of both sides to find DE:

DE = √32

DE = 4√2

So, the length of DE is 4√2 units.