Triangle ABC ~ Triangle ADE
AD=5; DB=3.5; BC=5.1; AE=6; EC=x
What is the length of AB?
What is the length of DE?
Write an expression that represents AC?
What is the length of EC?
What is the length of AC?
How do you get DB and EC? There are separate triangles. Apparently they have one point (A) in common.
To solve this problem, we can use the concept of similarity of triangles. When two triangles are similar, their corresponding sides are proportional.
Given that Triangle ABC is similar to Triangle ADE, we can set up proportions using their corresponding sides.
1. Length of AB:
Since Triangle ABC is similar to Triangle ADE, we can set up the proportion:
AB / AD = BC / DE
Substituting the given values, we have:
AB / 5 = 5.1 / DE
To solve for AB, cross-multiply and solve for AB:
AB = (5.1 * 5) / DE
2. Length of DE:
Using the same proportion, we can solve for DE:
AB / AD = BC / DE
Substituting the given values, we have:
5 / 5 = 5.1 / DE
To solve for DE, cross-multiply and solve for DE:
DE = (5.1 * 5) / 5
3. Expression for AC:
Since Triangle ABC is similar to Triangle ADE, the ratio of their sides is the same. So, we can write the expression for AC as:
AC = (AB / AD) * AE
4. Length of EC:
Given that EC = x, there is no direct information about its length in the problem statement. We need additional information to determine the length of EC.
5. Length of AC:
Using the expression for AC derived above, we can substitute the known values to find the length of AC.