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ZanzabumX [31]
2 years ago
13

Below is a magic square, meaning that the sum of the numbers in each row, in each column, and in each of the $2$ main diagonals

are equal. What is the value of $n$? [asy]size(125); for(int i = 0; i<4; ++i) { draw((0,i)--(3,i),linewidth(1)); } for(int j = 0; j<4; ++j) { draw((j,0)--(j,3),linewidth(1)); } label("$n-2$",(.5,.5)); label("3",(.5,1.5)); label("$n+2$",(.5,2.5)); label("$n+3$",(1.5,.5)); label("$n-1$",(1.5,1.5)); label("$1$",(1.5,2.5)); label("$2$",(2.5,.5)); label("$2n-5$",(2.5,1.5)); label("$n$",(2.5,2.5)); [/asy]
Mathematics
1 answer:
Mariulka [41]2 years ago
4 0

The property  of equality of the rows, columns, and diagonals in the magic

square can be used to find the value of <em>n</em>.

The value of <em>n</em> is 6

Reasons:

The magic square can be presented as follows;

\begin{array}{|c|c|c|}n-2&3&n + 2\\n + 3&n - 1&1\\2&2 \cdot n - 5&n\end{array}\right]

Given that the sum of the numbers in each row and in each column and in

each of the two diagonals are equal, to find the value of <em>n</em>, two rows having

different number of the variable <em>n</em> can be equated as follows;

The top row = n - 2 + 3 + n + 2 = The bottom row = 2 + 2·n - 5 + n

n - 2 + 3 + n + 2 = 2 + 2·n - 5 + n

2·n + 3 =  3·n - 3

3·n - 3 = 2·n + 3 (symmetric property)

3·n - 2·n = 3 + 3

n = 6

Learn more here:

brainly.com/question/17355019

brainly.com/question/20477897

brainly.com/question/8183549

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What is the value of x, when 10(x + 2) = 5(x + 8)?
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[0,2]

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