Respuesta :
Answer:
Similar triangles states that the two triangles are similar if their corresponding sides are in proportion.
As per the statement:
The perimeter of smaller triangle CDE is 133.
Since, triangles CDE and NOP are similar.
Corresponding are in proportion i.e
[tex]\frac{CD}{NO}=\frac{DE}{OP}=\frac{CE}{NP}[/tex]
It is also given that the length of two corresponding sides on the triangles are 53 and 212.
⇒[tex]\frac{CD}{NO}=\frac{DE}{OP}=\frac{CE}{NP} =\frac{53}{212}[/tex]
then;
[tex]\frac{\text{Perimeter of triangle CDE}}{\text{Perimter of triangle NOP}} =\frac{53}{212}[/tex]
⇒[tex]\frac{133}{\text{Perimter of triangle NOP}} =\frac{53}{212}[/tex]
By cross multiply we get;
[tex]133 \cdot 212 = 53 \cdot \text{Perimter of triangle NOP}[/tex]
Divide both sides by 53 we get;
[tex]\text{Perimter of triangle NOP} = \frac{133 \cdot 212}{53} =532[/tex]
Therefore, the perimeter of triangle NOP is 532
