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?

Video Solution

Solution Steps

00:00 Find the length of AB so that the triangle areas match

00:03 We'll examine the size of sides and lines according to the given data

00:12 Perpendicular according to the given data

00:17 AD is also the height in the triangle

00:20 We'll use the formula for calculating triangle area

00:25 (height multiplied by base) divided by 2

00:38 We'll substitute appropriate values and solve for the area

00:51 This is the triangle area

01:01 Let's calculate the triangle area using height and other side

01:07 We'll substitute appropriate values and solve for AB

01:27 Multiply by denominator to eliminate the fraction

01:32 Isolate AB

01:42 Simplify as much as possible

01:48 And this is the solution to the problem

Step-by-Step Solution

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:

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

$AB=10$