Question

50 m of fencing is used to make three sides of a rectangular area, using an existing wall as the fourth side. The area of the rectangle is 150 m².
Determine the dimensions of the rectangular area.

Answer 1

Answer:

• about 7.0 by 21.5 m
• about 43.0 by 3.5 m

Step-by-step explanation:

You want the dimensions of a 150 m² rectangle with a 3-sided perimeter of 50 m.

Setup

Let x represent the side of the rectangle parallel to the fourth-side wall, and y the distance out from the wall. Then the relations between the dimensions are ...

  x +2y = 50
  x·y = 150

Solution

Solving for y by substituting for x, we have ...

  (50 -2y)(y) = 150

  2y² -50y +150 = 0 . . . . . . . subtract the left-side expression

  y² -25y +75 = 0 . . . . . . . . divide by 2

  (y -12.5)² +75 -12.5² = 0 . . . . complete the square

  y = 12.5 ± √81.25 ≈ {3.486, 21.514}

Corresponding values of x are ...

  x = 50 -2y ≈ {43.028, 6.972}

The rectangular area may be 3.5 m wide by 43.0 m deep, or 21.5 m wide by 7.0 m deep. ("Wide" is the dimension parallel to the wall.)