Answer:
Area of the common pasture = 12 acres
Step-by-step explanation:
Let the dimensions of the farm owned by Jay are 'a' units and 'b' units.
Area of the farm = ab = 2 acres
Similarly, areas of the farm owned by Peter with dimensions 'a' unit and 'c' unit = ac = 4 acres
And area of the farm owned by Sam with dimensions 'b' and 'd' units = bd = 6 acres
Now, [tex]\frac{ab}{ac}=\frac{2}{4}[/tex]
[tex]\frac{b}{c}=\frac{1}{2}[/tex] ---------(1)
[tex]\frac{ab}{bd}=\frac{2}{6}[/tex]
[tex]\frac{a}{d}=\frac{1}{3}[/tex] ---------(2)
[tex]\frac{b}{c}\times \frac{a}{d}=\frac{1}{2}\times \frac{1}{3}[/tex]
[tex]\frac{ab}{cd}=\frac{1}{6}[/tex]
cd = 6(ab)
cd = 6 × 2 [Since ab = 2 acres]
= 12 acres
Therefore, area of the common pasture will be 12 acres.
