Answer:
Option: B is the correct answer.
B. 18 cm and 24 centimeters
Step-by-step explanation:
We know that if two triangles are similar than the ratio of the corresponding sides of the two triangles are equal.
i.e. if there is a triangle with side lengths a,b and c units respectively and other triangle with the corresponding side lengths a',b' and c' respectively.
Then for two triangles to be similar we have:
[tex]\dfrac{a}{a'}=\dfrac{b}{b'}=\dfrac{c}{c'}[/tex]
Here we have:
Juan drew a right triangle with leg length of 6 centimeters and 8 centimeters .
Now we will check in each of the options whose ratio are equal:
A. 9 centimeters and 16 centimeters
[tex]\dfrac{6}{9}=\dfrac{2}{3}[/tex]
and [tex]\dfrac{8}{16}=\dfrac{1}{2}[/tex]
As [tex]\dfrac{2}{3}\neq \dfrac{1}{2}[/tex]
Hence, option: A is incorrect.
B. 18 cm and 24 centimeters
[tex]\dfrac{6}{18}=\dfrac{1}{3}[/tex]
and [tex]\dfrac{8}{24}=\dfrac{1}{3}[/tex]
As both the ratios are equal.
Hence, option: B is correct.
C. 16 centimeters and 18 centimeters
[tex]\dfrac{6}{16}=\dfrac{3}{8}[/tex]
and [tex]\dfrac{8}{18}=\dfrac{4}{9}[/tex]
As [tex]\dfrac{3}{8}\neq \dfrac{4}{9}[/tex]
Hence, option: C is incorrect.
D. 3 centimeters and 5 centimeters
[tex]\dfrac{6}{3}=\dfrac{2}{1}[/tex]
and [tex]\dfrac{8}{5}[/tex]
As [tex]\dfrac{2}{1}\neq \dfrac{8}{5}[/tex]
Hence, option: D is incorrect.
