The length of a rectangle is nine inches more than its width. Its area is 486 square inches. Find the width and length of the rectangle.

Step-by-step explanation:

The relations between length (L) and width (W) are ...

  W +9 = L

  LW = 486

Substituting gives ...

  (W+9)W = 486

  W^2 +9W -486 = 0 . . . put in standard form

  (W +27)(W -18) = 0 . . . . factor

  W = 18 . . . .  the positive solution

The width of the rectangle is 18 inches; the length is 27 inches.

_____

Comment on factoring

There are a number of ways to solve quadratics. Apart from using a graphing calculator, one of the easiest is factoring. Here, we're looking for factors of -486 that have a sum of 9.

486 = 2 × 3^5, so we might guess that the factors of interest are -2·3² = -18 and 3·3² = 27. These turn out to be correct: -18 +27 = 9; (-18)(27) = -486.

Step-by-step explanation:

Given:

Initial distance, Di = 14.2 m

Final distance, Df = 2.3 m

Distance fallen = Di + Df

= -14.2 + (-2.3)

= -16.5

-16.5 tells us the total distance danny had fallen and the direction of the fall that is, 16.5 m from the origin.