Math  /  Geometry

Question7. Harold wants to build five identical pigpens, side by side, on his farm A using 30 m of fencing. Determine the dimensions of the enclosure that would give his pigs the largest possible area. Calculate this area.

Studdy Solution
Substitute x=2.5 x = 2.5 back into the equation for y y :
y=153(2.5) y = 15 - 3(2.5) y=157.5 y = 15 - 7.5 y=7.5 y = 7.5
Calculate the maximum area:
A=5(2.5)(7.5) A = 5(2.5)(7.5) A=5×18.75 A = 5 \times 18.75 A=93.75 A = 93.75
The dimensions that give the largest possible area are 2.5 2.5 meters for the width and 7.5 7.5 meters for the length, resulting in a maximum area of:
93.75 m2 \boxed{93.75 \text{ m}^2}

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