Leo's garden, which is 6m wide, has the same area as Jen's garden, whichis 8m wide. Find the length of the two rectangular gardens if Leo's garden is 3m longer than Jen's garden.

length of Leo's garden --- x

area of Leo's garden = 6x

length of Jen's garden --- x-3
area of Jens's garden = 8(x-3)

the area are the same, so
8(x-3) = 6x
8x - 24 = 6x
2x = 24
x = 12
Leo's garden is 12 m long
Jen's garden is 9 m long

check: 6(12) = 9(8)

Let's assume the length of Jen's garden is denoted by L meters.

According to the given information, Leo's garden, which is 6m wide, has the same area as Jen's garden, which is 8m wide. This can be expressed as:

6 * L = 8 * 8

Now, let's solve for L:

6L = 64

Dividing both sides of the equation by 6:

L = 64 / 6

L = 10.67 (rounded to two decimal places)

Since the length of a garden cannot be a decimal value, we can assume that the length of Jen's garden is 10 meters.

Given that Leo's garden is 3m longer than Jen's garden, the length of Leo's garden would be:

10 + 3 = 13 meters

Therefore, the length of Jen's garden is 10 meters, and the length of Leo's garden is 13 meters.

To find the length of the two rectangular gardens, we can use the formula for the area of a rectangle, which is length multiplied by width.

Given that Leo's garden is 6m wide and it has the same area as Jen's garden, which is 8m wide, we can represent the width of both gardens as 6m. Let's denote the length of Jen's garden as L meters.

Since Leo's garden is 3m longer than Jen's garden, we can represent the length of Leo's garden as L + 3 meters.

Now, we can calculate the area of each garden:

The area of Leo's garden is the product of its length and width: (L + 3) * 6.

The area of Jen's garden is the product of its length and width: L * 8.

Since the areas of both gardens are the same, we have the equation:

(L + 3) * 6 = L * 8

To solve for L, let's simplify the equation:

6L + 18 = 8L

Subtract 6L from both sides:

18 = 2L

Divide both sides by 2:

L = 9

Therefore, Jen's garden has a length of 9 meters. Since Leo's garden is 3m longer, his garden has a length of 9 + 3 = 12 meters.

So, Jen's garden is 9m long and 6m wide, while Leo's garden is 12m long and 6m wide.