Question

Triangle ABC $ are equilateral triangles A( ABC) :A( DEF) =1:2.if AB=4 then what is the length of DE?

Answer 1

Answer:

The side length DE=4√2

Step-by-step explanation:

The area of an equilateral triangle= (√3÷4)×a²

Where a is the side length

Side length of triangle ABC=4

Unknown side length of triangle DEF=x

Since the ratio of the area of two triangles=1:2

1÷2=16÷x²

x²=32

x=4√2

Answer 2

Answer:

DE = 4√2

Step-by-step explanation:

Triangle ABC $ are equilateral triangles A( ABC) :A( DEF) =1:2.if AB=4 then what is the length of DE?

ΔABC ≅ ΔDEF

ΔABC is an equilateral triangle

so AB = BC = CA = 4

Area of ΔABC = (√3/4) Side² = (√3/4) 4² = 4√3

Area of ΔABC : Area of ΔDEF = 1:2

=> Area of ΔABC / Area of ΔDEF = 1/2

=> Area of ΔDEF  = 2 * Area of ΔABC

=> Area of ΔDEF  = 2 * 4√3

=> Area of ΔDEF  = 8√3

ΔDEF is an equilateral triangle

so DE = EF = FD = x

Area of ΔDEF = (√3/4) x²

(√3/4) x² = 8 √3

=> x² = 32

=> x = √32

=> x = 4√2

DE = 4√2