Question

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

Answer 1

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

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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.)