Question

Please help, I've been trying for an hour and I don't know how to set up this problem.

Francois is a farmer who wants to build fences. Specifically, he wants to fence in his wife's rectangular vegetable garden and their children's smaller rectangular herb garden. The ratio of the width of Francois's wife's vegetable garden to its length is 5:8, and the ratio of the width of the herb garden to its length is 3:5. The length of the herb garden is, coincidentally, the same as the width of the vegetable garden. Francois finds that he will need 252 ft of fencing materials to fence in the separate gardens. (The gardens do not touch one another, nor are they near any other fences or buildings that can take the place of fencing materials.) What are the dimensions (length and width) of each garden?

Write a linear equation (hopefully in one variable) that could be used to solve this problem. (2pts)

Define your variable(s). (1pt)

Solve the equation for the variable that you have chosen. You need not show your work. (1pt)

Respond to the question. (1pt)

(The formula for the perimeter of a rectangle is given as: P=2l+2w)

Answer 1

Answer:30ft,18

48,13

Explanation:

Answer 2

Given ratio of the width of Francois's wife's vegetable garden to its length is 5:8.

Let l1,w1 be the length and width of Francois's wife's vegetable garden.

Then
`(w1)/(l1)  = (5)/(8)`

Given ratio of the width of the herb garden to its length is 3:5.

Let l2,w2 be the length and width of herb garden.

That is
`(w2)/(l2) = (3)/(5)`

Given that length of the herb garden is same as the width of the vegetable garden.

That is l2=w1 let this common value be x.

So, first ratio is
`(x)/(l1)=(5)/(8)`

l1 =
`(8x)/(5)`

Second ratio is
`(w2)/(x) = (3)/(5)`

w2 =
`(3x)/(5)`

perimeter of vegetable garden = 2(l1+w1) =
`2((8x)/(5) +x) = 2*(13x)/(5)  = (26x)/(5)`

Perimeter of herb garden = 2(l2+w2) =
`2(x+(3x)/(5) ) = 2*(8x)/(5) =(16x)/(5)`

Given that francois has 252ft of fencing material.

That is perimeter of vegetable garden + perimeter of herb garden = 252

`(26x)/(5) +(16x)/(5)  = 252`

`(42x)/(5) =252`

`x = (252*5)/(42) = 30 feet`

So,
`l1 = (8x)/(5) = (8*30)/(5) = 48 feet`

And
`w2 = (3x)/(5) = (3*30)/(5) = 18 feet`

So dimensions of vegetable garden are 48ft, 30ft.

And dimensions of herb garden are 30ft,18ft.