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17 votes
17 votes
The lengths of the sides of a square are multiplied by 3.5. How is the ratio of the areas related to the ratio of the side lengths?

A. The ratio of the areas is the square of the ratio of the side lengths.
B. The ratio of the areas is the same as the ratio of the side lengths.
c. The ratio of the areas is the cube of the ratio of the side lengths.
d. The ratio of the areas is the square root of the ratio of the side lengths.

User Setempler
by
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2 Answers

20 votes
20 votes

Answer:

A. The ratio of the areas is the square of the ratio of the side lengths. Is correct.

Hope this helps!

User Gpmurthy
by
3.2k points
11 votes
11 votes

Answer:

A The ratio of the areas is the square of the ratio of the side lengths.

Explanation:

10 x 3.5 = 35 and would be the same size each

35 x 35 = 1225

Ratio of areas = 10x10 and 10x3.5 x 10 x 3.5 = 100 : 1225 = 4: 49

Therefore just from doing this we can find easily by referring back to ratio above shown.

D IS NOT TRUE This means the ratio of the areas (1225) is the square root of the ratio (sqrt1225=35) of the side lengths (35:35) is not true

sqrt 1225 is 35 and becomes a square root of the area

Where matching this to ratio of sides is not true as 35:35= 1:1 and the ratio to the sides are not the same as ratio of two areas. But when we square we get the answer right.

when we cross multiply (division) we find find the ratio of areas 100:1225 is NOT TRUE AND NOT SAME AS ratio 10:35

We therefore left with DIVIDING THE ratio SIDES AS SIMPLIFIED into the Areas ABOVE to show-

1225/49 = 25 same here we have the area same ratio as

100/4 = 25 same

10:35 = 3.5^2 + 3.5^2 =12.50 + 12.50 = 25

A IS TRUE. as when we square the ratio 1=3.5 and add them together 1=3.5^2 +3.5^2 we get answer = 25

User Bens Steves
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2.9k points
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