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.)
