Final answer:
To find the dimensions of Bosco's garden, we set up a system of equations based on the area of the garden (200 m²) and the amount of fencing available (50 m). By expressing one variable in terms of another and substituting into the area equation, we can solve for the garden's dimensions using algebraic methods.
Step-by-step explanation:
Bosco wishes to start a 200 m² rectangular vegetable garden and has 50 m of barbed wire to fence three sides, with his house compound wall acting as the fourth side. To find the dimensions of the garden, we can use the area formula for a rectangle (Area = length × width) and the perimeter formula for three sides (Perimeter = length + 2×width), given that one side is already provided by the wall.
Let's assume the length of the garden that runs along the wall is 'l' meters and the width is 'w' meters. The total length of barbed wire used for the three sides would be 'l + 2w' meters. Since Bosco has 50 m of barbed wire, the equation will be:
l + 2w = 50
Furthermore, we have the area of the garden, which is 200 m². The equation for the area is:
l × w = 200
To solve these two equations simultaneously, we can express one variable in terms of the other from the first equation and substitute it into the second equation. Let's solve for 'w' from the first equation:
w = (50 - l) / 2
Now substitute 'w' in the area equation:
l × ((50 - l) / 2) = 200
After solving the quadratic equation, we find the dimensions of the garden that meet the conditions. Without knowing the exact values, we can demonstrate that the process involves algebraic manipulation and quadratic equation solving methods.