Find the perimeter and the side of a square where length of a diagonal is 40cm
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Let 'a' be the length of the side of the square. AC is a diagonal.
Perimeter of square ABCD = 4 a units
4a=40cm[given]
a=
4
40
=10cm
We know that in a square each angle is 90
o
and the diagonals are equal.
In △ABC,AC
2
=AB
2
+BC
2
=10
2
+10
2
=100+100=200
∴AC=
200
=
2×100
=10
2
=10×1.414=14.14cm
Diagonal AC = Diagonal BD
Hence, Sum of the diagonals =14.14+14.14=28.28cm.
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