Find the side and perimeter of a square whose diagonal is 10cm
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refer the attachment
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Refer the attachment for the figure.
Let AB = BC = x
AC = 10
Angle ABC = 90° ... angle of square
Using Pythagoras theorem,
AC^2 = AB^2 + BC^2
10^2 = x^2 + x^2
100 = 2x^2
50 = x^2
√50 = x
5√2 = x
So, Each side of square is 5√2 cm
Perimeter of square = 4 × side
= 4 × 5√2
= 20√2 cm
So, Side of square is 5√2 cm and Perimeter of square is 20√2.
Let AB = BC = x
AC = 10
Angle ABC = 90° ... angle of square
Using Pythagoras theorem,
AC^2 = AB^2 + BC^2
10^2 = x^2 + x^2
100 = 2x^2
50 = x^2
√50 = x
5√2 = x
So, Each side of square is 5√2 cm
Perimeter of square = 4 × side
= 4 × 5√2
= 20√2 cm
So, Side of square is 5√2 cm and Perimeter of square is 20√2.
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