Question

Farmers Jay, Peter, and Sam own rectangular farms, as indicated in the figure. Jay owns 2 acres of land, Peter owns 4 acres and Sam owns 6 acres. Find the area of the common pasture. PLEASE HELP ASAP!

Answer 1

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, $\frac{ab}{ac}=\frac{2}{4}$

$\frac{b}{c}=\frac{1}{2}$ ---------(1)

$\frac{ab}{bd}=\frac{2}{6}$

$\frac{a}{d}=\frac{1}{3}$ ---------(2)

$\frac{b}{c}\times \frac{a}{d}=\frac{1}{2}\times \frac{1}{3}$

$\frac{ab}{cd}=\frac{1}{6}$

cd = 6(ab)

cd = 6 × 2 [Since ab = 2 acres]

    = 12 acres

Therefore, area of the common pasture will be 12 acres.