The length of a rectangle is 2 feet more than the width. find the dimensions of the rectangle if its area is 63 square feet

You want to find factors of 63 that differ by 2.
.. 63 = 1*63 = 3*21 = 7*9

The last pair of factors differ by 2, so your dimensions are
.. length: 9 feet
.. width: 7 feet


If you want to write an equation, you can let w represent the width. Then the area is
.. A = width*length
.. 63 = w*(w +2)
.. w^2 +2w -63 = 0
To factor this, you need to find two factors of -63 that add to +2. -7 and +9 are those factors (see above).
.. (w -7)(w +9) = 0
.. w = 7 or -9 . . . . . . . only the positive solution is of interest
width = 7 feet
length = 9 feet

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You could let x represent the average of length and width. Then your equation for area is
.. A = width*length
.. 63 = (x -1)(x +1) = x^2 -1
.. 64 = x^2
.. 8 = x
The width is 8-1 = 7; the length is 8+1 = 9. (Both dimensions have units of feet.)