(c) If the perimeter of a square is 40 cm, find (i) the length of a diagonal, and (ii) its area.
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Answer:
d=14.14cm area =160 cm
Step-by-step explanation:
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=440=10cm
We know that in a square each angle is 90o and the diagonals are equal.
In △ABC,AC2=AB2+BC2
=102+102=100+100=200
∴AC=200
=2×100=102
=10×1.414=14.14cm
Diagonal AC = Diagonal BD
Hence, Sum of the diagonals =14.14+14.14=28.28cm.
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