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

Area of the common pasture = 12 acres

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,
`(ab)/(ac)=(2)/(4)`

`(b)/(c)=(1)/(2)` ---------(1)

`(ab)/(bd)=(2)/(6)`

`(a)/(d)=(1)/(3)` ---------(2)

`(b)/(c)* (a)/(d)=(1)/(2)* (1)/(3)`

`(ab)/(cd)=(1)/(6)`

cd = 6(ab)

cd = 6 × 2 [Since ab = 2 acres]

= 12 acres

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