xercise
5. If the sum of each row, column and
diagonals are equal, then the value of pa
rand s respectively, is
19
18
16.
S
15
(1) 2017. 14.22
(3) 14.17.20.22
2) 17.20.14 22
4. 20. 14. 17. 22
Answers
Answer :-
Ncert solutions
Grade 7
Mathematics
Science
Chapters in NCERT Solutions - Mathematics, Class 7
Exercises in Integers
Question 6
Q7) In a magic square each row, column and diagonal have the same sum. Check which of the following is a magic square.
(i)
(ii)
Solution
Transcript
solution 7: (i)
Sum of the rows
Row 1 = 5+\left(-1\right)+\left(-4\right)5+(−1)+(−4)
5-1-4\ =\ 05−1−4 = 0
Row 2 = \left(-5\right)+\left(-2\right)\ +7(−5)+(−2) +7
-5-2+7\ \ =0−5−2+7 =0
Row 3 = 0+3+\left(-3\right)0+3+(−3)
0+3-3\ \ =0\ 0+3−3 =0
Sum of the columns
Column 1 = 5+\left(-5\right)+05+(−5)+0
5-5+0\ =\ 05−5+0 = 0
Column 2 = \left(-1\right)+\left(-2\right)+\ 3\ (−1)+(−2)+ 3
-1-2+3\ \ =\ 0−1−2+3 = 0
Column 3 = \left(-4\right)+7\ +\left(-3\right)(−4)+7 +(−3)
-4\ +7\ -3\ \ =\ 0−4 +7 −3 = 0
Sum of the diagonals
Diagonal 1
\left(5\right)+\left(-2\right)+\left(-3\right)(5)+(−2)+(−3)
5-2-3\ \ =\ 05−2−3 = 0
Diagonal 2
\left(-4\right)+\left(-2\right)\ +0\ (−4)+(−2) +0
-4-2+0\ =\ -6−4−2+0 = −6
Box (i) is not a square because all the sums not equal.
(ii)
Sum of the rows
Row 1 = 1+\left(-10\right)\ +01+(−10) +0
1-10+0\ =-91−10+0 =−9
Row 2 = \left(-4\right)+\left(-3\right)+\left(-2\right)(−4)+(−3)+(−2)
-4-3-2\ \ \ =\ -9−4−3−2 = −9
Row 3 = \left(-6\right)+4+\left(-7\right)(−6)+4+(−7)
-6+4-7\ \ =\ -9−6+4−7 = −9
Sum of the columns
Column 1 = 1+\left(-4\right)+\left(-6\right)1+(−4)+(−6)
1-10\ =-91−10 =−9
Column 2 = \left(-10\right)+\left(-3\right)+4(−10)+(−3)+4
-10\ -3+4\ \ =\ -9−10 −3+4 = −9
Column 3 = 0+\left(-2\right)+\left(-7\right)0+(−2)+(−7)
0-2-7\ \ =\ -90−2−7 = −9
Sum of the diagonals
Diagonal 1
1+\left(-3\right)+\left(-7\right)1+(−3)+(−7)
1-10\ =\ -9\ 1−10 = −9
Diagonal 2
0+\left(-3\right)+\left(-6\right)0+(−3)+(−6)
-3-6\ =\ -9−3−6 = −9
Box (ii) is a magic square because all the sums are equal.
I hope that is helpful