Arectangle has an area of 1050 square feet. its width is eight feet less than twice the length. find the measures of the length and width of the rectangle.

Step-by-step explanation:

If L represents the length, then the width is (2L-8) and the area is ...

  A = LW

  1050 = L(2L-8)

  525 = L(L-4) . . . . . divide by 2

Completing the square, we have ...

  525 +4 = L² -4L +4 . . . . . add the square of half the L coefficient

  529 = (L -2)² . . . .simplify

  ±23 = L -2 . . . . . . take the square root

  L = 25 . . . . . . . the negative root doesn't work in this scenario

  (2L-8) = 42 . . . width

The length is 25 feet; the width is 42 feet.

answer by yourhope:

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