Question

Triangle LMN ~ Triangle PON. What is the value of x?

Answer 1

Step 1 :

In this question, we can see clearly that:

`\text{Triangle LMN }\approx\text{ Triangle PON}`

Step 2:

From the diagram, we can see that :

`(MN)/(LM)\text{ = }(ON)/(OP)`

where MN = x,

LM = 42,

ON = 12,

OP = 14.

Step 3:

Substituting the values, we have that:

`\begin{gathered} (x)/(42)\text{ = }(12)/(14) \\ \text{cross - multiply, we have that:} \\ 14\text{ x = 12 ( 42 )} \\ \text{Divide both sides by 14 , we have that:} \end{gathered}`
`\begin{gathered} x\text{ = }\frac{12(\text{ 42 )}}{14} \\ x\text{ = 12 x 3} \\ \text{x = 36 - OPTION D} \end{gathered}`

CONCLUSION :

The value of x = 36 -- OPTION D .