Question

The perimeter of two similar triangles $\mathrm{ABC}$ and $\mathrm{LMN}$ are $60$ $cm$and $48$ $cm$ respectively. If $\mathrm{LM}=8$ $cm$, then what is the length of $\mathrm{AB}$ ?

Answer 1

Step 1: Applying a property of similar triangles

If the two triangles are similar then, the ratio of the perimeter of similar triangles is equal to the ratio of their corresponding sides.

If $\mathrm{ABC}$ and $\mathrm{LMN}$ are two similar triangles then,

$\frac{AB}{LM}=\frac{BC}{MN}=\frac{AC}{LN}=\frac{Perimeterof∆ABC}{Perimeterof∆LMN}$

Step 2: Substituting the given value

Given:

$Perimeterof∆ABC$ =$60$ $cm$

$Perimeterof∆LMN$ = $48$ $cm$

$\mathrm{LM}=8$ $cm$

$\frac{AB}{8}=\frac{60}{48}$

$AB=\frac{60\times 8}{48}$

$AB=10$

Thus, we can conclude that the length of $\mathrm{AB}$ is $10cm$.