Please help with the top question !

9514 1404 393

  13.3 m

Step-by-step explanation:

Let d represent the length of the diagonal. Then the length of the rectangle is (d-2) and the width is (d-6). The area is the product of length and width, so is ...

  A = LW

  83 = (d -2)(d -6) = d² -8d +12

  71 = d² -8d . . . . . . . . subtract 12 to get the constant out of the way

  d² -8d +16 = 87 . . . . add (-8/2)² = 16 to both sides to complete the square

  (d -4)² = 87 . . . . . . . write as a square

  d -4 = √87 . . . . . . . positive square root

  d = 4 +√87 ≈ 13.3 . . . . add 4

The diagonal is about 13.3 meters long.

Additional comment

If you check to see if the side lengths actually correspond to those of a rectangle, you find that they do not. The geometry described here is impossible. The rectangle with the proposed relations between sides and diagonal would have a diagonal of about 12.899 m and an area of about 75.19 m².

a

step-by-step explanation:

a