Question

∆ABC and ∆DEF are equilateral triangles A(∆ABC) : A(DEF) = 1.2. if AB = 4 then what is length of DE? ❎No Spam​

Answer 1

Answer:

Length of the side DE is 4√2

Step-by-step explanation:

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Answer 2

Answer:

4√2

Step-by-step explanation:

Given that ∆ABC and ∆DEF are equilateral triangles A(∆ABC) : A(DEF) = 1.2. if AB = 4.

Draw a line perpendicular X and Y in both ∆ABC and DEF.

Now,

In ∆ABX and ∆DEY (equilateral triangle)

/_B = /_C = 90°

/_AXB = /_DYE (by construction)

∆ABX ~ ∆DYE

Therefore,

AB/DE = AX/DY (corresponding sides of similar triangle)

(Ar. ∆ ABC)/(Ar. ∆DEF) = 1/2

(1/2 × b × h)/(1/2 × b × h) =1/2

(1/2 × AB × AX)/(1/2 × DE × DY) = 1/2

(1/2 × 2AB²)/(1/2 × DE²) = 1/2

As, AB/DE = AX/DY

So,

(AB²)/(DE²) = 1/2

(4)²/(DE²) = 1/2

16/DE² = 1/2

DE² = 32

DE = 4√2

Therefore, the length of DE is 4√2