Question

Find out the missing number of the magic square.

17		11
	14
17		11

Answer 1

Hint: In magic square, the sum of rows, column and diagonal remains the same.

Complete step by step answer:
(1) Calculate sum of diagonal first as all its terms are known
$$17+14+11=42$$

 (2) Let $x$ be the value in first rows

17	$$(x)$$	11
	14
17		11

$$\begin{gathered} \therefore x+17+11=42 \\ x+28=42 \\ x=42-28 \\ x=14 \end{gathered}$$

(3) Now, let y be the missing value in the 1st column.

17	14	11
$$(y)$$	14
17		11

$$\begin{gathered} \therefore 17+y+17=42 \\ \Rightarrow 34+y=42 \\ \Rightarrow y=42-34 \\ y=8 \end{gathered}$$

(4) Now, let $z$ be the missing value in third row

17	14	11
8	14
17	$$(z)$$	11

$$\begin{gathered} \therefore 17+z+11=42 \\ \Rightarrow 28+z=42 \\ \Rightarrow z=42-28 \\ z=14 \end{gathered}$$

17	14	11
8	14
17	14	11

(5) Now, let $t$ be the missing value in the 3rd column.

17	14	11
8	14	$$(t)$$
17	14	11

$$\begin{gathered} \therefore 11+t+11=42 \\ \Rightarrow t+22=42 \\ \Rightarrow t=42-22 \\ t=20 \end{gathered}$$
This is the required magic square.

Note: To find the length of the diagonal of a square, multiply the length of one side by the square root of $2$, if the length of one side is $x$. The diagonals of a square intersect (cross) at $$90$$ degree angle, this means that the diagonals of the square are perpendicular.