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Surface Area and Volume, Part 2

How would you solve these problems? Ratios in Surface Area?

For instance, if there are 15 ham sandwiches on a table and 12 cheese sandwiches, the ratio of ham sandwiches to cheese sandwiches is 15/12 15 over 12, or in simplest terms, 5/4 5 over 4. This ratio can also be written as 5:4 (5 to 4) and is read as "5 to 4." So, for every five ham sandwiches on the table there are four cheese sandwiches.

For two integers, a and b, where b ≠ 0, all of the following are true.

1. A ratio may be written as a over a/b, a:b, “a to b”

2. The ratio a over b equals 1 if a equals a = b

Where a and b are greater than 0,

3. The ratio a/b (a over b) > 1 if a > b

4. The ratio a/b < 1 if a < b

Suppose you are given a rectangle with length 2 cm and width 1 cm. The perimeter is 6cm, and the area is 2cm². If you doubled one of the sides of the rectangle, such as the width, what do you think would happen to the perimeter and the area? What would happen if you now doubled the length, too? Write a 4-6 paragraph essay on your response. Use examples to support your response.

You may have noticed that if both dimensions of the rectangle are doubled, then the perimeter also doubles and the area increases by a multiplier of 4, or 2².