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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?

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 class=

Sagot :

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

[tex]\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}}[/tex]

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

[tex]\frac{13.5}{9}=\frac{10.5}{7}=\frac{7.5}{5}=1.5[/tex]

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