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3 votes
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

2 Answers

2 votes

(16)/(14)=(8)/(7)=8:7-ratio\ of\ perimeters\\\\8^2:7^2=64:49-ratio\ of\ areas\\\\Answer:A.
User James Wahlin
by
8.3k points
1 vote

Answer:

A


Explanation:

Two lengths of similar figures relates by the scale factor
k.

Two areas of similar figures relates by the scale factor
k^(2).


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


A=kB

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


A=k^(2)B


So we can write:


16=k(14)\\k=(16)/(14)=(8)/(7)


Since, perimeter is also length, the ratio would be
(8)/(7)

Similarly, ratio of their areas should be
(8^2)/(7^2)=(64)/(49)

Answer choice A is right.

User Nikesha
by
7.8k points