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
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
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
l1 =
Second ratio is
w2 =
perimeter of vegetable garden = 2(l1+w1) =
Perimeter of herb garden = 2(l2+w2) =
Given that francois has 252ft of fencing material.
That is perimeter of vegetable garden + perimeter of herb garden = 252
So,
And
So dimensions of vegetable garden are 48ft, 30ft.
And dimensions of herb garden are 30ft,18ft.