Brianna purchased a box with a base diagonal length that is 45 centimeters long. What are two possible pairs of dimensions for the length and width of the box?

One pair: Length = 31.82 cm and Width = 31.82 cm

Other pair: Length = 30 cm and Width = 33.54 cm

Step-by-step explanation:

The base of the box has a shape of a rectangle, and to find the length of the diagonal, we can use the pythagoras theorem as follows:

D^2 = L^2 + W^2

Where D is the diagonal, L is the length and W is the width.

If we assume the base of the box to be a square, we can find one pair of dimension:

L = W

D^2 = L^2 + L^2 = 2L^2

D = 1.414*L

D = 45 -> 1.414*L = 45 -> L = 45/1.414 = 31.82 cm

So one pair is length = 31.82 cm and width = 31.82 cm

To find other pair, we can just assume a value for the length, so:

Length = 30 cm

Then we can find the width:

45^2 = 30^2 + W^2

W^2 = 2025 - 900 = 1125

W =  33.54 cm

So the other pair is Length = 30 cm and Width = 33.54 cm

1/800 is the right answer