In a 3 x 4 dot rectangle there are 10 dots on the outside and 2 dots on the inside.In a 4 x 5 dot rectangle there are 14 dots on the outside and 6 dots on the inside.How may dots are outside in a 1989 x 1990 dot rectangle?
To find the number of dots outside in a 1989 x 1990 dot rectangle, we can first analyze the given information.
In the 3 x 4 dot rectangle, there are 10 dots on the outside and 2 dots on the inside. This means that there are 12 total dots in the rectangle.
In the 4 x 5 dot rectangle, there are 14 dots on the outside and 6 dots on the inside, totaling 20 dots.
We can observe that the number of dots on the outside increases by 4 when we increase the length of the rectangle by 1, and the number of dots on the inside increases by 4 when we increase the length of the rectangle by 1.
Using this pattern, we can calculate the number of dots on the outside for a 1989 x 1990 dot rectangle.
First, find the difference in length between the given 4 x 5 dot rectangle and the desired 1989 x 1990 dot rectangle:
1989 - 4 = 1985
Next, multiply this difference by 4 to calculate the number of dots on the outside of the longer side of the rectangle:
1985 * 4 = 7940
Finally, add the number of dots on the outside of the 4 x 5 dot rectangle (14) to find the total number of dots on the outside of the 1989 x 1990 dot rectangle:
14 + 7940 = 7954
Therefore, there are 7954 dots on the outside of a 1989 x 1990 dot rectangle.
2x3 rectangle, the inside is 1x2
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4x5 rectangle, the inside is 2x3
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3x6 rectangle, the inside is 1x4
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Have you discovered the formula to calculate a 1989 x 1990 dot rectangle?