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?
What is the length of base BC, in cm?
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
DE is the segment above BC. Can you help?
I already told you that
the 3rd segment is √3/2 BC
so all the other sides are in the same ratio
Thank you!
Why did the triangle go to the dance party?
Because it wanted to show off its base moves!
To find the length of the base BC, we need to determine the length of the segments that divide the triangle into four equal parts.
Let's denote the length of the base BC as x.
Since the longest of these segments is 36 cm, it divides the triangle into three equal parts. Therefore, the length of each of the three smaller segments is also 36 cm.
In total, we have four segments: one with length 36 cm and three with length 36 cm each. So, the total length of the segments is:
36 cm + 36 cm + 36 cm + 36 cm = 4 * 36 cm = 144 cm
The sum of the lengths of the segments is equal to the length of the base BC. Therefore:
x = 144 cm
Thus, the length of the base BC is 144 cm.
Now, let's move on to the second question about the ratio of the dimensions of triangle ADE to the dimensions of triangle ABC.
Without specific information about the lengths of the sides of triangles ADE and ABC, we cannot determine the exact ratio of their dimensions. We need more information to calculate this.
The dimensions of a triangle can refer to its side lengths, angles, or area. So, if you provide more details about the sides, angles, or any other relevant information about triangles ADE and ABC, I can help you calculate the ratio of their dimensions.