In the second year of junior high school, I just learned the Pythagorean theorem

You don't have a picture, how can you help!

I still can't see it.

Cut the cylinder along the high line with a knife, which is equivalent to a rectangle.

The height is 12cm, and the bottom radius is 3cm.

The length of the rectangle is the circumference of the bottom surface of the cylinder = 2 r = 2 * 3 * 3 = 18 cm (take 3 in the question).

The width of the rectangle is the height of the cylinder = 12 cm

Therefore, the ab distance is the diagonal length drawn in the figure = under the root number (9 + 12) = 15 cm, so the shortest distance that needs to be crawled is 15 cm

PS: After looking at the picture drawn by lz, I found that the previous one was written wrong, point B should indeed be at the middle point of the length, and the triangle is a right triangle composed of 9, 12, and 15.

Because the line segment between two points is the shortest.

Therefore, the side of the cylinder is formed into a rectangle, and the circumference of the ground with a length of 2 r = 2 * 3 * 3 = 18 and a width of 12 is 12

The shortest distance to crawl is squared equal to 18 squared plus 12 squared = 468, so the shortest distance is about.

Put the sides of the cylinder, then the distance the ant climbs over is the diagonal of the rear rectangle.

The width of the rectangle is the height of the cylinder, and the length is the circumference of the bottom surface of the cylinder.

Circumference = 2 r = 2 3 3 = 18 cm.

12 squared plus 18 squared = 468 under the root

Because the shape of the cylinder in this problem is rectangular:

Then the length of the rectangle obtained from the cylinder is: l=2 r=2x3x3=18cm, and the width of the rectangle obtained from the cylinder is: d=12cm

Ant on the bottom side of the cylinder ant, want to eat food at point B opposite the bottom of point a, even if the diagonal in the rectangle:

So l = (18x18+12x12) = 468

The Pythagorean theorem is a basic geometric theorem that states that the sum of the squares of the two right-angled sides of a right triangle is equal to the square of the length of the side of the hypotenuse (i.e., the "string"). That is, assuming that the two right-angled sides of a right-angled triangle are a and b, and the hypotenuse is c, then a +b = c.

For example, in a right-angled triangle, the right-angled side a=3, b=4, and the hypotenuse c=5, it is easy to find a +b =c, that is, 3 +4 =5 =25

Many times you can understand and learn mathematical theorems through examples, and I hope you will learn and improve

a^2+b^2=c^2

The Pythagorean theorem is to memorize the public and then do all kinds of problems.

If you are proficient in doing it, you will be able to do anything.

Method 1: Let b c be 3x 5x then there is 8*8+(3x)*(3x)=(5x)*(5x) to solve x=2, i.e., a=8; b=6,c=10

Method 2: Since there is a three-sided ratio of the Pythagorean theorem, there is a ratio of 3:4:5, and when there is a ratio of 3:5, then the ratio of the third side has a short side of 8, and there must be a length of the remaining two sides of 6 and 10

From the Pythagorean theorem: c = b +a

b:c=3:5

So b = 3 5c

Bringing in the formula gives 8 +(3 5c) =c

i.e. 64+9 25c =c

c = 100 c = 10 so b = 6

Solution: Let b=3x, then c=5x

According to the Pythagorean theorem:

c²=b²+a²

5x)²=（3x)²+8²

25x²-9x²=64

16x²=64

x²=4x=2b=3x=6

c=5x=10

I can't do it with the hook bone theorem in junior high school, I can only solve it with the knowledge of trigonometric functions in high school: pass a to make the parallel lines of bc, and then solve the trapezoidal and triangle respectively (where the formula triangle area s=1 2absinc (both sides and angles)) is used, and finally the answer I get is (61 4) root number 3

Use the cut-and-fill method.

Passing the point D as the parallel line of BC Crossing the point A and D as the perpendicular lines of BC respectively and crossing the two points E and F to obtain a rectangle.

Find the area of the three triangles that you make up separately and subtract them from the area of the rectangle.

The midline on one side is half his.

So it's a right triangle, and this side is hypotenuse.

Let the right-angled sides be a, b, and the hypotenuse c

c=2a+b+c=2+√6

a+b=√6

square a + b + 2ab = 6

Pythagorean theorem. a²+b²=c²=4

So 4+2ab=6

ab=1, so area=ab2=1 2