snooki
Answered

Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

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]

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.