In daily life, we are no stranger to each other. The parade queue on October 1 is a square array, and the queue formed by broadcasting exercises in schools is also a square array. The square matrix problem has been mostly involved in recent years' examinations. Such questions are not difficult, and it can be said that they can be grasped by simple review. Public education is here to give pointers.
A square matrix with n people on each side:
Example 1. Existing batches of square floor tiles. If a large square is assembled, there will be 62 pieces left. If an additional piece is added to each side, 37 pieces will be missing.
A.2433 B.2459 C.2463 D.2475
Method 2: It is known that adding 37 floor tiles can form a large square, indicating that the total number of floor tiles + 37 is a square number, and only the C term plus 37 is a square number of 2500. It is not recommended to use "-62" to verify whether it is a square number, because after subtracting 62, it is not easy to see at a glance whether the result is a square number, and the C term is correct.
[Public Dial] When you want to find the total number of people in a square matrix, you can find n or use the characteristics of the square to do the problem.
Example 2. A village is currently carrying out afforestation activities, and the planted trees are arranged in a square matrix. The outermost trees are known to be 60, so this square matrix has a total of trees ().
A.272 B.256 C.225 D.240
[Chinese Public Analysis] The outermost tree is 60, according to the formula: the outermost number of people = 4n-4, that is, 4n-4 = 60, the solution is n = 16, the total number required = n2 = 256, and the B term is correct .
Regarding the rectangular square matrix, you can make an analogy based on the square square matrix, so it is much easier to learn.
Example 3. A sports meeting needs to organize a square matrix with equal length and width. The organizer arranged a square of fresh flowers and a square of colored flags. After the two squares were admitted, they formed a square. The people of the square of flowers formed the outermost circle of the new square. It is known that there are 28 more bunting squares than flowers squares, and the total number of new squares is ().
A.100 B.144 C.196 D.256
In addition to the common square and rectangular square matrices, there is also a type of triangular matrix. Because of its low frequency, it only appeared in the 2019 national exam. :
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