If the diagonal of square is #12sqrt2# cm then perimeter of square is?

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Answer 1 · 2018-03-15T14:48:40

the perimeter #=48# cm

Tony B

Using Pythagoras

#x^2+x^2=(12sqrt(2))^2#

#2x^2=(12sqrt(2))^2#

Divide both sides by 2

#x^2=(12sqrt(2))^2/2#

Square root both sides

#x=(12sqrt(2))/sqrt(2) = 12xxsqrt2/sqrt2#

But #sqrt2/sqrt2=1#

#x=12# cm# larr" 1 side of the square"#
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The perimeter if 4 lots of #x# cm which is 4 lots of 12 cm

So the perimeter #=4xx12 "cm"=48# cm