Triangle ABC: Finding AB Length When AD=6, CE=3, and CB=5

Given the triangle ABC

AD=6 CE=3 CB=5

What should be the length of AB so that the area of a triangle ABC is compatible with the rest of the data in the drawing?

Given that AD is perpendicular to CB

We can establish that AD is the height of the triangle ADB

Hence the formula for the area of triangle ABC=

$\frac{AD\times CB}{2}$

We insert the existing data into the formula:

$\frac{6\times5}{2}=\frac{30}{2}=15$

Due to the fact that CE is also a height, we can calculate the area of triangle ABC as follows:

$\frac{CE\times AB}{2}$

Since we found the area of triangle ABC, we will insert the data into the formula:

$15=\frac{3\times AB}{2}$

We then multiply across:

$30=3AB$

Lastly we divide both sides by 3:

$\frac{30}{3}=\frac{3AB}{3}$

$AB=10$