Question

The two triangles drawn are similar. Find the length of side x.32 miС10 mi8 miAB6 mi24 miThe two triangles drawn are similar. Find the length of side x ?

Answer 1

when two triangles are similar it means that both of them share a relation between their sides, and it must be fulfilled on all of its sides.

In order to find x, we need to find first the relationship with a pair of sides that is complete.

We can use sides AB and (AB)'

Then,

`\begin{gathered} AB=k\cdot(AB)^(\prime) \\ 6=k\cdot24 \\ k=(6)/(24) \\ k=(1)/(4) \end{gathered}`

then use this proportion to find x

`\begin{gathered} AC=k\cdot(AC)^(\prime) \\ 10=(1)/(4)\cdot x \end{gathered}`

solve the resulting equation for x

`\begin{gathered} 10\cdot4=x \\ x=40 \end{gathered}`

the missing side is equal to 40.