Question

NOP has side lengths 5cm, 7cm and 9cm. If NOP is similar to RST, which of the following could be lengths of the sides of RST?

Answer 1

Given that the triangles are similar, then their corresponding sides must be in proportion, that is,

`\frac{\text{longest side NOP}}{\text{longest side RST}}=\frac{intermediate\text{ side NOP}}{intermediate\text{ side RST}}=\frac{\text{shortest side NOP}}{\text{shortest side RST}}`

Substituting with the option, 7.5 cm, 10.5 cm, and 13.5 cm, we get

`(13.5)/(9)=(10.5)/(7)=(7.5)/(5)=1.5`