Respuesta :
Answer:
The options b) ,c) and e) are correct
The three choices shows the ratio of the area of the smaller rectangle to the area of the larger rectangle are b)[tex](\frac{4}{16})^2[/tex] , c) [tex]\frac{12}{192}[/tex] and e) [tex](\frac{3}{12})^2[/tex]
Step-by-step explanation:
Given that a large rectangle has a length of 16 and width of 12.
A smaller rectangle has length of 4 and width of 3
To show the ratio of the area of the smaller rectangle to the area of the larger rectangle:
we know that "If two figures are similar, the the ratio of its areas is equal to the scale factor squared"
From the given scale factor is [tex]\frac{1}{4}[/tex]
Let z be the scale factor
Let x be the area of the smaller rectangle
Let y be the area of the large rectangle
[tex]z^2=\frac{x}{y}[/tex]
Since scale factor is [tex]\frac{1}{4}[/tex] hence [tex]z=\frac{1}{4}[/tex]
we have [tex]z^2=(\frac{1}{4})^2[/tex]
[tex]=\frac{1}{16}[/tex]
∴ [tex]z^2=\frac{1}{16}[/tex]
Now show that the ratio of the area of the smaller rectangle to the area of the larger rectangle with each options.
a) [tex]\frac{4}{16}[/tex]
[tex]\frac{4}{16}=\frac{1}{4}[/tex]
Compare with [tex]\frac{1}{16}[/tex] we get,
[tex]\frac{1}{4}\neq \frac{1}{16}[/tex]
Hence it is not possible.
b) [tex](\frac{4}{16})^2[/tex]
[tex](\frac{4}{16})^2=\frac{16}{256}[/tex]
[tex]=\frac{1}{16}[/tex]
Compare with [tex]\frac{1}{16}[/tex] we get,
[tex]\frac{1}{16}=\frac{1}{16}[/tex]
This implies that the ratio of the area of the smaller rectangle to the area of the larger rectangle.
c) [tex]\frac{12}{192}[/tex]
[tex]=\frac{1}{16}[/tex]
Compare with [tex]\frac{1}{16}[/tex] we get,
[tex]\frac{1}{16}=\frac{1}{16}[/tex]
This implies that the ratio of the area of the smaller rectangle to the area of the larger rectangle.
d) [tex](\frac{4}{12})^2[/tex]
[tex]=\frac{16}{144}[/tex]
[tex]=\frac{1}{9}[/tex]
Compare with [tex]\frac{1}{16}[/tex] we get,
[tex]\frac{1}{9}\neq \frac{1}{16}[/tex]
Hence it is not possible.
e) [tex](\frac{3}{12})^2[/tex]
[tex]=\frac{9}{144}[/tex]
[tex]=\frac{1}{16}[/tex]
Compare with [tex]\frac{1}{16}[/tex] we get,
[tex]\frac{1}{16}=\frac{1}{16}[/tex]
This implies that the ratio of the area of the smaller rectangle to the area of the larger rectangle.
∴ options b) ,c) and e) are correct
The three choices shows the ratio of the area of the smaller rectangle to the area of the larger rectangle are b)[tex](\frac{4}{16})^2[/tex] , c) [tex]\frac{12}{192}[/tex] and e) [tex](\frac{3}{12})^2[/tex]
Answer:
The other individual who answered the question is correct, please give them 5 stars and a thanks.
Step-by-step explanation:
To simplify and clarify, the answers are B, C, E
