Harvard May 22, 2013
Question: Write a blog entry for the following prompt: Your neighbor has a
backyard with an area 450 square feet. He decides to place a sandbox for his
children in a section of his backyard which is 32 square feet. Determine the
perimeter of your neighbors back yard, as well as the perimeter of the
sandbox. (Hint: adding simplified radicals is similar to adding fractions – like
radicals can be combined!) In your response we sure to clearly articulate your
thinking as to your process for solving, as well as a justification for your
reasoning.
Answer: The perimeter of my neighbor's back yard is 60 Ö2 ft because each side of the yard is 15 * Ö2 feet long. Therefore, by adding 15 * Ö2 four times and the perimeter is 60 Ö2 ft long.
450
Ö25 * Ö18
5 * Ö18
5 * Ö9 * Ö2
5 * 3 * Ö2
15 * Ö2
Perimeter = l+w+l+w
(15 * Ö2) + (15 * Ö2) + (15 * Ö2) + (15 * Ö2) = 60 Ö2 ft
Answer: The perimeter of the sandbox is 16 * Ö2 ft because each side of the sandbox is 4 * Ö2 ft long. That is to say, by adding 4 * Ö2 four times, the perimeter would be 60 * Ö2 .
32
Ö4 * Ö8
2 * Ö8
2 * Ö4 * Ö2
2 * 2 * Ö2
4 * Ö2
Perimeter = l+w+l+w
(4 * Ö2) + (4 * Ö2) + (4 * Ö2) + (4 * Ö2) = 16 Ö2
