The group is planning to build a fence around the garden. How many yards of fencing materials do they need for the fence? Show your work.

They need 130 yards to build up the fence.

Step-by-step explanation:

Attached you can find a picture that will guide the explanation. We will assume that each line is supposed to be a fence. We will assume also that the diagonals that cross any sub field that has the same vegetable is unnecessary.  That is that the diagonal of the tomatoes and the watermelon are not going to be built.

Recall that the red peppers area is a right triangle. So, using pythagora's theorem, we have that

b^2 + 12^2= 15^2 so b= 15^2-12^2

which gives us that b = 9.

On the same fashion, the diagonal of the spinach-celery sector is . Recall that the field is a rectangle, so the perimeter of the outter fence is 2*(12+6)+2*(8+9) = 70 yds. Then, the total perimeter is given by

outter fence (70)+

fence spinach-watermelon (8) +

fence red peppers-watermelon(12)+

fence red peppers-carrots (15)+

fence carrots-tomatoes (9)+

fence celery-tomatoes(6) +

fence spinach-celery(10)

= 130 yds

(if the diagonals of tomatoes and watermelon are added, the same procedure applies. watermelon diagonal is 14.42 yds and tomatoes diagonal is 10.81 yds)