Question

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

Answer 1

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 $\frac{w1}{l1} = \frac{5}{8}$

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 $\frac{w2}{l2} = \frac{3}{5}$

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 $\frac{x}{l1}=\frac{5}{8}$

l1 = $\frac{8x}{5}$

Second ratio is $\frac{w2}{x} = \frac{3}{5}$

w2 = $\frac{3x}{5}$

perimeter of vegetable garden = 2(l1+w1) = $2(\frac{8x}{5} +x) = 2*\frac{13x}{5} = \frac{26x}{5}$

Perimeter of herb garden = 2(l2+w2) = $2(x+\frac{3x}{5} ) = 2*\frac{8x}{5} =\frac{16x}{5}$

Given that francois has 252ft of fencing material.

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

                                    $\frac{26x}{5} +\frac{16x}{5} = 252$

                                               $\frac{42x}{5} =252$

                                                  $x = \frac{252*5}{42} = 30 feet$

So, $l1 = \frac{8x}{5} = \frac{8*30}{5} = 48 feet$

And $w2 = \frac{3x}{5} = \frac{3*30}{5} = 18 feet$

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

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