Question

A rectangular garden has links twice as great as it's with a second rectangular garden has the same link as the first garden and with that is for meters greater than the width of the first garden the second Gordon has area of 120 m² what is the length of the two gardens

Answer 1

For the bigger rectangle

Width of bigger rectangle = W

Length of bigger rectangle, L = 2W

For the smaller rectangle

Width , w = W+4

Length, l = L = 2W

Area, a =120
`m^2`

Now we know,

Area = length x width

`$a=l * w$`

`$120=(2W) * (W+4)$`

`$120=2W^2 + 8W$`

`$2W^2+8W-120=0$`

`$W^2+4W-60=0$`

`$(W+10)(W-6) = 0$`

We get, either
`W=-10` (rejecting)

or
`W=6`

∴ length of the bigger rectangle,
`$L=2W $`

= 2(6)

= 12 m

Length of the smaller rectangle,
`$L=2W$`

= 2(6)

= 12 m

Hence, the length of the two gardens is 12 m.