Question

If AB=12,AC=16, and ED=5, find AE,

Answer 1

The length of AE is 15/4 units, or 3.75 units.

To find the length of AE, we can use the concept of similar triangles and proportions. First, let's set up a proportion using the given information:

AB = 12

AC = 16

ED = 5

We have two similar triangles: ABE and ACE. The sides of these triangles are proportional because angle A is common to both triangles (angle ABE is congruent to angle ACE). Therefore, we can set up the following proportion:

(AB / AC) = (AE / ED)

Now, plug in the values:

(12 / 16) = (AE / 5)

Now, cross-multiply:

12 × 5 = 16 × AE

60 = 16 × AE

To solve for AE, divide both sides by 16:

AE = 60 / 16

Simplify the fraction:

AE = 15 / 4

So, the answer is 15/4 units, or 3.75 units.

Answer 2

Applying the triangle similarity theorem, the length of AE in the image shown is: AE = 15.

How to apply the triangle similarity theorem?

The triangles in the image attached below are similar by the AA similarity theorem, this therefore means that their corresponding side lengths are proportional to each other, which is:

AC/AB = AD/AE

Given that:

AC = 16

AB = 12

AD = AE + 5

AE = ?

Plug in the values:

16/12 = AE + 5 / AE

4/3 = AE + 5 / AE

4AE = 3(AE + 5)

4AE = 3AE + 15

4AE - 3AE = 15

AE = 15