Question

Triangle ABC and triangle DEF are equilateral triangles. A( triangleABC) :A( triangle DEF) = 1:9, AB= 9,then DE=​

Answer 1

Given: Δ ABC and Δ DEF are Equilateral triangles.

ar(Δ ABC) : ar(Δ DEF) = 1:9

AB = 9

To find length of DE.

We know that All Equilateral triangles are similar to each other.

So, we use a result which states that,

If two triangles are similar then ratio of the area of triangles is equal to square to the ratio of the corresponding sides.

So we have,

Δ ABC / Δ DEF = (AB / DE)²

=> 1/9 = ( 9 / DE )²

=> 1/9 = 81 / DE²

=> DE² = 81 × 9

=> DE² = 729

=> DE = (✓729)

=> DE = 27

Therefore, Length of the side DE is 27 .

I hope this was helpful to you

Answer 2

ANSWER:

DE = 27

(Refer from attachment)