Question

The rectangle is
  
enter your response here units long and
  
enter your response here units wide.

Answer 1

I don’t have the missing numbers or a diagram — can you paste the image or tell me the given information (area, perimeter, diagonal, coordinates, grid lengths, etc.)?

If you’re looking for how to find length and width from common givens, here are quick methods:

- If you know area A and perimeter P:
Let L = length and W = width. Then
L + W = P/2 and L·W = A.
Solve t^2 − (P/2)t + A = 0 for t; the two roots are L and W.
Example: A = 24, P = 20 → L + W = 10, LW = 24 → t^2 − 10t + 24 = 0 → t = 6 and 4.

- If you know area A and diagonal d:
L·W = A and L^2 + W^2 = d^2. Use (L+W)^2 = d^2 + 2A to get L+W = sqrt(d^2 + 2A), then solve as above.

- If you know diagonal d and one side (say W):
L = sqrt(d^2 − W^2).

- If you have coordinates of opposite corners (x1,y1) and (x2,y2) with sides aligned to axes:
width = |x2 − x1|, length = |y2 − y1| (or vice versa).

Tell me the numbers or upload the picture and I’ll fill in the blanks.