The area of triangle ABC is divided into four equal parts by segments parallel to the base BC. DC is 36 cm. A is the top point of the triangle.
What is the ratio of the dimensions of triangle ADE to the dimensions of triangle ABC?
Notice you have similar triangles.
In more than one of your previous posts, I have shown you that the
areas of similar shapes are proportional to the SQUARES of their corresponding sides.
Apply that principle here.
I see. I understand now. Thanks for your support.
To find the ratio of the dimensions of triangle ADE to triangle ABC, we need to determine the length of DE in relation to the length of BC.
Since triangle ABC is divided into four equal parts by parallel segments, we can deduce that DE is equal to one-fourth of BC.
Given that DC is 36 cm, we can find BC by using the properties of similar triangles. Triangle DCE is similar to triangle ABC since they share the same angles and have parallel sides. Therefore, we can set up the following proportion:
DC/DE = BC/BC
Substituting the given values, we have:
36 cm/DE = BC/BC
Simplifying further, we get:
36 cm/DE = 1/1
Since DE is equal to one-fourth of BC, we can substitute DE with (1/4)BC:
36 cm/(1/4)BC = 1/1
Multiplying both sides of the equation by (1/4)BC, we get:
36 cm = BC
Therefore, the dimensions of DE are one-fourth of BC, which means DE is 9 cm.
The ratio of the dimensions of triangle ADE to triangle ABC is 9 cm : 36 cm, which can be simplified to 1 : 4.
To find the ratio of the dimensions of triangle ADE to the dimensions of triangle ABC, we first need to determine the dimensions of triangle ABC.
Let's denote the height of triangle ABC as h and the length of the base as b.
Since the area of triangle ABC is divided into four equal parts by segments parallel to the base BC, each of these segments divides the height of the triangle into four equal parts as well.
Given that DC is 36 cm, we know that the entire height of triangle ABC is 4 times DC, which is equal to 4 times 36 cm, or 144 cm (36 cm * 4).
Now, let's find the dimensions of triangle ADE.
Since triangle ADE and triangle ABC have a parallel base, we know that their bases have the same length, which is b.
The height of triangle ADE is equal to the height of triangle ABC divided by 4, since the area is divided into four equal parts. Therefore, the height of triangle ADE is 144 cm divided by 4, which is equal to 36 cm (144 cm / 4).
So, the dimensions of triangle ADE are a base length of b (same as triangle ABC) and a height of 36 cm.
To find the ratio of the dimensions of triangle ADE to the dimensions of triangle ABC, we can simply compare their heights:
Ratio of heights = height of triangle ADE / height of triangle ABC
= 36 cm / 144 cm
= 1/4
Therefore, the ratio of the dimensions of triangle ADE to the dimensions of triangle ABC is 1:4.