Given DC = 7, CB = 8, AB = 1/4 AD, and ED = 4/5 AD, find FC. Express your answer as a decimal.
not sure how to tackle this one
not enough information.
Do these point lie in on a straight line?
Do the points fall in order of A,B,C,... ?
To solve this problem, we can use the concept of similar triangles. By analyzing the given information, we can see that triangle ABC is similar to triangle EDC. This means that their corresponding sides are proportional.
First, let's determine the length of AD:
Since AB = 1/4 AD, we can rewrite this as AD = 4 AB.
Given AB = 1/4 AD, we can substitute this into the equation to get:
AD = 4 * (1/4 AD)
AD = AD
From this, we can see that AD is equal to AD, which means that we cannot determine its length from the given information. However, we can still find the value of FC by focusing on the proportion of the sides.
Using the fact that triangle ABC is similar to triangle EDC, we can set up the proportion:
AB / ED = BC / DC
Plugging in the given values, we get:
(1/4 AD) / (4/5 AD) = 8 / 7
To simplify the left side of the equation, we can multiply both the numerator and denominator by 4 AD:
(1/4 AD) * (5 AD / 4 AD) = 8 / 7
5 / 16 = 8 / 7
Cross-multiplying, we have:
5 * 7 = 8 * 16
35 = 128
However, this equation does not hold true, which means that there was an error in the setup or the provided information. As a result, we cannot determine the value of FC without additional information.