Some math help please?

Question

I'm in Geometry honors and we got a review packet due tomorrow.

I forgot how to do one of the problems on there for whatever reason.

It goes:

"A baseball diamond is actually a square with each side 90 feet long. If a ball is thrown along the diagonal of the square from home plate to second base, which is closest to the distance the ball travels?

F 90 feet

G 90 [square root] 2 feet

H 100 feet

I 100 [square root] 2 feet

If you could tell me how to work this problem along with the answer I would appreciate it , because I want to know how to do problems like these for future reference.

Answer 1

Pythagorean Theorem is what's useful here.

(Diagonal of a square is the hypotenuse of 1 of the 4 triangles we can form in there)

c² = a² + b²

c² = 90² + 90²

c² = 16200

c²^½ = 16200^½

c = 127.2792206...

So now we know the length is approximately 127 feets, we will calculate the rest and see which one is the closest to 127.

F 90 (no)

G 90 * SR of 2 = 127.2792206 (that's it)

There's no need to continue as G is the exact answer.

Hope I helped you!

Answer 2

Basically you have a right triangle with 2 sides being 90 and the hypotenuse being the distance you are looking for.

c^2 = a^2 + b^2

c^2 = 90^2 + 90^2

c^2 = 2(90^2)

c = 90(sqrt(2)) feet

G

Answer 3

You have to draw a square with sides labeled 90 feet long.

Now draw a diagonal across two opposite points on the square.

Now disregard two of the lines of the square and so that you just see the remaining triangle.

You want to find how long the long side, or hypotenuse of the triangle is. You should also know that the hypotenuse equals the square of the sum of the squares of the other two sides, or if the other sides are a and b and the hypotenuse is c, then c = √(a² + b²).

Now plug in the values you have for a and b: c = √(90² + 90²); c=90√2 feet.