Final answer:
To find the length of one side of a perfect square, divide the perimeter by 4. The correct length and perimeter pairs are 21 and 84, and 19 and 76. The pairs 18 and 70, and 44 and 441 are incorrect because the perimeters do not match the length of one side times four.
Step-by-step explanation:
To find the length of one side of a perfect square, we must understand that all sides are equal in length. Therefore, if we were given the perimeter of a square, we could find the length of one side by simply dividing the perimeter by 4 since a square has four sides of equal length. For example, if a perfect square has a perimeter of 84, we divide 84 by 4 to find the length of one side, which would be 21 units.
The formula for the perimeter (P) of a square is P = 4a, where 'a' is the length of one side. The formula to calculate the area of a square is A = a·a = a². Additionally, when dimensions are scaled up, we can find the new dimensions by multiplying the original dimensions by the scale factor.
Let's verify the options given:
- Length of a side 21 and the perimeter 84: 4 x 21 = 84. This is correct.
- Length of a side 19 and the perimeter 76: 4 x 19 = 76. This is correct.
- Length of a side 18 and the perimeter 70: 4 x 18 = 72. This is incorrect as the perimeter should be 72, not 70.
- Length of a side 44 and the perimeter 441: 4 x 44 = 176. This is incorrect as the perimeter should be 176, not 441, which instead represents the area since 44² = 441.