PERIMETER CHALLENGE
By: Zach G., Jennifer H., Peter P., Katie L., and Tyler T.
Problem (a)
Step 1: We read the instructions and the information that the problem gave us.
Step 2: Then we found out the longer side is 7 cm because we found out how many 13 cm blocks are in the 33 cm structure (there are 2).
Step 3: Then we multiplied 13x2=26 because two 13 cm blocks fit in to the structure.
Step 4: Then it came to us that 33-26= 7 which is the longer side of the small rectangle.
Step 5: We looked at the 13 cm block and since 13-7= 6 that means 2 shorter sides equal 6. Therefore the shorter side is 3 because 6\2 =3.
Step 6: We figured out the product of 7x2 and the product of 3x2 and we found the sum of the two products. Which is 20 cm.
Step 7: The answer is 20 cm.
Problem (b)
Step 1: We first read the information that they gave us.
Step 2: We found out those 3 short sides of the small rectangle equals 1 long side of the small rectangle.
Step 3: Then we found out that the area of the small rectangle is 12 square cm because 60\5= 12.
Step 4: Then we found all the factors of 12 and paired them up.
Step 5: The only paired factors that follow the principles of what was mentioned before is 6x2=12 which proves that the perimeter is 16 because (6x2)+(2x2)=16.
Step 6: the answer is 16 cm
Problem (c)
Step 1: We first read the information that they gave us.
Step 2: We found out those 4 short sides of the small rectangle equals one long side of the small rectangle.
Step 3: We found out that the area of the small rectangle is 100 square mm because 600\6=100.
Step 4: We found all of the factors of 100 and paired them up.
Step 5: We found out the only paired factors that follow the principles is (20x2)+(5x2)=50 which proves that the perimeter is 50 mm.
Step 6: The answer is 50 mm.
Problem (d)
Step 1:We read the area of shape (d), which was 180 square cm.
Step 2: We came up with the equation X= 4\5 of Y. In this equation X represents the shorter sides and Y represents the longer sides. This is true because the large rectangle equals either 5 shorter sides or 4 longer sides.
Step 3: With that in mind, we found out that the area is 20 square cm, because 9 small rectangles equal 1 large rectangle, and 180\9=20.
Step 4: We found all the factors of 20 and paired them up.
Step 5: We found out that only pair of the factors follows the principles mentioned above. The paired factors are 5 and 4.
Step 6: Which proves that the perimeter is 18.
Problem (e) Step 1: We looked at the problem and discovered that the answer could not be in number form.
Step 2: We started with A+B since there was already A and B.
Step 3: We added up the y-axis lines excluding the two C’s that are equal to another A.
Step 4: We added up the x-axis lines, which is equal to another B.
Step 5: With all the information that we have, equals 2(A+B+C)= the perimeter, which is 2A+2B+2C.
Step 6: The answer is 2A+2B+2C.