What is the diagonal of a rectangle with: length = 3 + square root of 2 width = 3 - square root of 2

Expert Answers

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For a rectangle with sides L and W the length of the diagonal is sqrt (L^2 + W^2)

In the question we have the following conditions:

L = 3 + sqrt 2

W = 3 - sqrt 2

Therefore teh length of the diagonal is

sqrt [ ( 3 + sqrt  2)^2 + ( 3 - sqrt 2)^2]

=> sqrt [ 9 + 2 + 6 sqrt 2 + 9 + 2 - 6 sqrt 2]

=> sqrt [ 22]

Therefore the diagonal is sqrt 22.

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