find the length of the diagonal of the rectangle ABCD where A(1,2) B(1,5) C(3,5) D(3,2)

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We have the rectangle  ABCD A(1,2) B(1,5) C(3,5) D(3,2)

Let us calculate lenghth and width:\

AB = sqrt(1-1)^2 - (5-2)^2] = sqrt3^2 = 3\

BC = sqrt[(3-1)^2 + (5-5)^2] = sqrt2^2 = 2

CD = sqrt[(3-3)^2 + (5-2)^2] = sqrt3^2 = 3

AD = sqrt[(3-1)^2 + (2-2)^2] = sqrt2^2 =...

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We have the rectangle  ABCD A(1,2) B(1,5) C(3,5) D(3,2)

Let us calculate lenghth and width:\

AB = sqrt(1-1)^2 - (5-2)^2] = sqrt3^2 = 3\

BC = sqrt[(3-1)^2 + (5-5)^2] = sqrt2^2 = 2

CD = sqrt[(3-3)^2 + (5-2)^2] = sqrt3^2 = 3

AD = sqrt[(3-1)^2 + (2-2)^2] = sqrt2^2 = 2

Then we have the length (L) = 3  and width (W) = 2

Then the diaginal is:

 d = sqrt(L^2 + W^2)

    = sqrt(9 + 4) = sqrt13

==> The diagonal length is d= sqrt13

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