snooki
Answered

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The widths of two similar rectangles are 16 cm and 14 cm. What is the ratio of their perimeters? Of their areas?
a.
8:7 and 64:49
b.
9:8 and 64:49
c.
8 and 81-64
d.
8:7 and 81:64

Sagot :

[tex]\frac{16}{14}=\frac{8}{7}=8:7-ratio\ of\ perimeters\\\\8^2:7^2=64:49-ratio\ of\ areas\\\\Answer:A.[/tex]
TaeKwonDoIsDead

Answer:

A


Step-by-step explanation:

Two lengths of similar figures relates by the scale factor [tex]k[/tex].

Two areas of similar figures relates by the scale factor [tex]k^{2}[/tex].


  • If length of one figure is A, and corresponding length of another figure is B, then they are related by:

[tex]A=kB[/tex]

  • If area of one figure is A, and corresponding Area of another figure is B, then they are related by:

[tex]A=k^{2}B[/tex]


So we can write:

[tex]16=k(14)\\k=\frac{16}{14}=\frac{8}{7}[/tex]


Since, perimeter is also length, the ratio would be [tex]\frac{8}{7}[/tex]

Similarly, ratio of their areas should be [tex]\frac{8^2}{7^2}=\frac{64}{49}[/tex]

Answer choice A is right.

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