A rectangle with sides 9 cm and 1 cm has the same diagonal as a square. What is the length of the side of the square? Give your answer as a surd.

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Answer 1 · 2018-04-22T12:48:29

The side length of the square is #a=sqrt(41)# units.

The length of the diagonal of rectangle, according to Pythagoras' Theorem, will be given by:

#sqrt(9^2+1^2)=sqrt(82)#

The diagonal of square with side length '#a#" is #sqrt2#a.

In this case:

#sqrt2a=sqrt82#

#a=(sqrt(82))/(sqrt(2))#

#a=sqrt41#