Question

The area of triangle ABC is divided into four equal parts by segments parallel to the base BC. The longest of these segments is 36 cm. What is the length of base BC?

What is the ratio of the dimensions of triangle ADE to the dimensions of triangle ABC?

Answer 1

What is the length of base BC, in cm?

Answer 2

since the area of similar triangles scales by the ratio squared,
the shortest segment is 1/2 BC, making the area above it 1/4 of ABC
the 2nd segment is 1/√2 BC, making the area above it 1/2 of ABC
the 3rd segment is √3/2 BC, making the area above it 3/4 of ABC
so √3/2 BC = 36
BC = 72/√3

No idea where DE is

Answer 3

DE is the segment above BC. Can you help?

Answer 4

I already told you that
the 3rd segment is √3/2 BC

so all the other sides are in the same ratio

Answer 5

Thank you!