Are you Smart Enough-Math?

Well if i figure out this questions answer i get 10 free points on my test..


A square fort of unknown dimensions has four gates. Gates are located at the center of each side of the fort. A tree was planted twenty yards due north of the north gate. Today, April decided to go for a walk on her lunch hour. If April exits the fort using the south gate and walks due south for fourteen yards and then turns westward and walks 1775 yards along a straight path, then this will be the first instance she will be able to view the tree. What is the shortest distance, rounded to the nearest yard, from her position to the tree?

 

Why are you asking us if we are smart to know this while you should know the answer?

 

Maybe he is bad at math and needs help.

 

What math are you in? It sorta sounds like you could use pythagorian theorem to figure this out, since the gates are all aligned, and it would be a right triangle.

This is what I would assume would be it, it's A^2 x B^2 = C^2, so 1775^2x41+x^2=c^2.



If I'm way off, my apologies.

-Edit-I used the wrong things on the first line, It's not 41, and the pictures side is off. I misread.

 

Well I suck at math that's why im posting this hear.


<--I'm currently in pre-calc and this is i think only algebra..

My college is doing this math thing that gives you free points if you answer right...

This is the second to hardest question....

So yea no clue what to do =[

 

I'm a genius and I was bored so here ya go:

After drawing this down and looking at it, you will notice that there are two main triangles that you need to take note of. The first one, lets say triangle A, is the triangle formed by the tree, the north gate, and the north-west corner of the fort. And triangle B, which is formed by the tree, the point where April changed direction from going south to going west, and the point where she was finally able to see the tree. Under the assumption that the sides of the fort are in perfect alignment with North, South, East, and West, we notice that triangle A is in ratio with triangle B since the north side of the fort splits triangle B horizontally. When you slice a right triangle horizontally or vertically, you end up with a miniature version of the original triangle, which is what happens in this case. Now lets say that half of a side of the fort is x, which makes the whole side 2x. So the base of triangle A is x and the vertical side is 20 , and the base of triangle B is 1775 and the vertical side is (20+14)+2x. Now all you have to do is plug in numbers for x until you find a value that satisfies both triangles. You'll find that x=125, and the ratio of the base to the vertical side being 1 to 6.25. Now all you have to do is plug x=125 in for triangle B and you'll get 284. Then use the Pythagorean theorem to find the hypotenuse and voila you have the answer.

 

Yup, pretty much killed it. Assuming you did the math right, everything else is set-up right.

 

I'm a certified genius but I'm too lazy to get a paper thats 2 feet away from me