Question

Triangle ABC is an equilateral triangle with the altitude of AD. Use the altitude to form a second equilateral triangle(triangle ADE). Use the alitude of triangle ADE to form a third equilateral triangle(triangle AFG) and then use the altitude of triangle AFG to form a fourth eqiulateral triangle(triangle AHK). What is the ration of the area of triangle ABC to the area of triangle AHK

Answer 1

Before I suggest something, do you know how to start this off or do you have any idea of how to approach this? @ineedhelpquick

Answer 2

@genius12 yea i know i can do it with pythagorean theorem and also with 30 60 90 triangles

Answer 3

mhm, you should also make use of the useful fact that given an equilateral triangle with side length 's', it's height is given by \(\bf h=\frac{\sqrt{3}}{2}s\) and its area is given by \(\bf A=\frac{\sqrt{3}}{4}s^2\)

Answer 4

It is also fairly easy to derive these formulae if you ever forget them.

Answer 5

holy crap im still in geometry i dont know that yet

Answer 6

@genius12

Answer 7

@genius12 this is the drawing

Answer 8

Ok so this is essentially a repetitive task but fairly straightforward. We only need to use the fact that the height of an equilateral triangle with side length 's' is \(\bf h=\frac{\sqrt{3}}{2}s\) and its area is \(\bf A=\frac{\sqrt{3}}{4}s^2\). Are you ok if I use these 2 facts because they'll make ur life alot easier?

Answer 9

@ineedhelpquick

Answer 10

the height is also the altitude right? @genius12

Answer 11

yup

Answer 12

ok thx @genius12

Answer 13

so u know wat to do from here right? @ineedhelpquick

Answer 14

yea somewhat @genius12