Question

Find the length of AB

Answer 1

The length of line segment AB is equal to 4 units.

How to find the missing side of a triangle

In this problem we need to determine the length of side AB in a system of two right triangles, which satisfy the following condition:
`\overline{AD} \cong \overline {DC}`. Then, by SAS theorem, triangles ABD and BCD are congruent, which means that sides AB and BC are also congruent:

`\overline{AB} \cong \overline {BC}`

Then, by definition of congruence we obtain the exact value of x:

AB = BC

2 · x = 5 · x - 6

3 · x = 6

x = 2

And the length of line segment AB:

AB = 2 · 2

AB = 4

Line segment AB has a length of 4 units.