Question

Points B and D lie on sides AC and AE such that BD is parallel to CE. If AB = 10, AD = 16, and DE = 22, then find the length of AC.

A) 42
B) 44
C) 46
D) 48

Answer 1

To find the length of AC, we can use the concept of similar triangles. By setting up a proportion and solving for the unknown length, we find that AC is equal to 12.25.

Step-by-step explanation:

To find the length of AC, we need to use the concept of similar triangles. Since BD is parallel to CE, we can see that triangle ABD is similar to triangle AEC.

Using the property of similar triangles, we can set up the following proportion:

AB/AD = EC/DE

Substituting the given values, we have:

10/16 = EC/22

Cross multiplying, we get EC = (10/16) * 22 = 13.75

Since AC = AB + BC, we can find the length of BC by subtracting EC from AD:

BC = AD - EC = 16 - 13.75 = 2.25

Therefore, the length of AC is AB + BC = 10 + 2.25 = 12.25