Question

In the triangles below, MLB = m

Answer 1

`6(2)/(3)`

Step-by-step explanation:

Given that:

`m\angle A=m\angle B,m\angle T=m\angle M`

Since the sum of interior angles of a triangle is 180 degrees,

`m\angle L=m\angle H`

By using the AAA theorem, "Two triangles have their corresponding angles equal if and only if their corresponding sides are proportional", the sides of the triangles LBT and HAM are proportional. So,

`(BT)/(AM)=(LB)/(HA)=(TL)/(MH)`

Substitute the given length of sides.

`(6)/(10)=(4)/(HA)=(5)/(MH)`

Consider

`(6)/(10)=(4)/(HA)`

Cross multiply to find HA.

`\begin{gathered} HA=4\cdot(10)/(6) \\ =(20)/(3) \\ =6(2)/(3) \end{gathered}`

So, the first option is correct.