The length of a rectangle is three units more than the width the area of the rectangle is 40 units what is the length in units of the rectangle

  8 units

Step-by-step explanation:

It can help to consider the divisors of 40:

  40 = 1×40 = 2×20 = 4×10 = 5×8

The pair of numbers in this list that differs by 3 is 5 and 8. The length is 3 units longer, so the length is 8 units.

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Alternate solution

Let L represent the length. Then the width is (L-3), and the area is the product of length and width:

  A = L(L-3)

  40 = L^2 -3L

We can "complete the square" by adding the square of half the L coefficient.

  40 +1.5^2 = L^2 -3L +1.5^2

  42.25 = (L -1.5)^2 . . . write the right side as a square

  6.5 = L -1.5 . . . . . . . take the positive square root

  8 = L . . . . . . . . . . . . add 1.5

The length of the rectangle is 8 units.