Question

you have 500 meters of fencing with which to make 2 enclosures. One enclosure will be in the shae of a square and the other will have the shape of an isosceles right triangle. For example the enclosures might look something like this (imagine a square next to a isosceles right triangle). How long should the legs of the triangle be to minimize the combined area of the two enclosures?

Answer 1

are there any answer choices?

Answer 2

no

Answer 3

I mean it seems that you dont have to use the whole 500 yards right?

Answer 4

or meters

Answer 5

you do have to use the whole 500 meters

Answer 6

That doesnt make, sense. That means the area cant be any less than 500 meters,

Answer 7

so theoretically you could just do 5 times 5 for the square one, and whatevr leg lengths to compensat for the 475 meters left

Answer 8

so you have to use all 500 meters to make 2 enclosures, one in the shape of a square and one in the shape of a isosceles right triangle. You have to dimension the legs of the triangle/square to get the to have the smallest combined area

Answer 9

@justjm

Answer 10

This one gave me a brain fart XD

Answer 11

The giveaway to how you need to approach is when it says 'isosceles right triangle'

Are they connected?

Answer 12

no

Answer 13

so since it is a square I can make one side x, which makes the perimeter of the square 4x.
I can make a leg on the isosceles right triangle y, so the perimeter of that becomes 2y+ y times sqrt of 2

Answer 14

correct, now you're getting there!

Answer 15

what do I do next

Answer 16

Are you allowed to use calculus or only precalculus methods?

Answer 17

I am in pre-calc. so pre-calc. only

Answer 18

Usually the teachers dont mind advanced usage of methematics. They definitely wouldnt change the grading

Answer 19

Man I cant type tonight

Answer 20

I don't know them though

Answer 21

True, good point

Answer 22

need help!!!

Answer 23

got the answer