The Pythagorean theorem is speed, oh, urgent

Let the side ab of an equilateral triangle be x, then ab is the square area of the side is x 2, and the height of the triangle bisects the other side, then the half side is x 2

Yes: x 2+(x 2) 2=3 2 - derived from the Pythagorean theorem, the sum of the squares of the two sides is equal to the square of the third side.

solution, get: x 2 = 36 5 = square centimeters.

Then, there is: ab is the square with the side and the area is the square centimeter.

The height is 3, so the length of the three sides is 2 and the number 3. So the square area is 12

Let the side ab of the equilateral triangle be x, because the equilateral triangle is three lines in one, so his high-scoring bottom edge = 1 2x, according to the Pythagorean theorem:

1 2x) + 3 = x square.

1 square of 4x + square of 9=x.

1 4x square - x square = -9

3 square of 4x = -9

The square of x = 12, and the three sides are the root number 12 .Square area = root number 12 times 4 = 4 root number 12 = 8 root number 3....

The first square and the tail are squared, and the product is multiplied by 2 times.

The square of a plus the square of b is equal to the square of c.

What is the formula for the Pythagorean theorem.

The Pythagorean theorem is a fundamental geometric theorem that states that the sum of the squares of the two right-angled sides of a right-angled triangle is equal to the square of the hypotenuse. In ancient China, the right triangle was called the Pythagorean shape, and the smaller of the right-angled sides was the hook, the other long right-angled side was the strand, and the hypotenuse was the chord, so this theorem was called the Pythagorean theorem, and some people called the Shanggao theorem.

The Pythagorean theorem now has about 500 ways to prove it, making it one of the most provable theorems in mathematics. The Pythagorean theorem is one of the important mathematical theorems discovered and proven by mankind in the early days, one of the most important tools for solving geometric problems with algebraic ideas, and one of the links between numbers and shapes. In China, Shang Gao during the Shang Dynasty proposed a special case of the Pythagorean theorem of "Pythagorean Three Strands, Four Xuanwu".

In the West, the Pythagoreans of ancient Greece in the 6th century BC were the first to propose and prove this theorem, who used the deductive method to prove that the square of the hypotenuse of a right triangle is equal to the sum of the squares of two right angles.

They are the edges corresponding to angles a, b, and c.

According to the square where the area ratio is equal to the similarity ratio, the area of the rectangle in the figure is equal to.

"The Pythagorean theorem: In any right triangle, the sum of the squares of the two right-angled sides must be equal to the squares of the hypotenuses. This theorem is also known as the "Shang Gao Theorem" in China and the "Pythagorean Theorem" in foreign countries.

The Pythagorean theorem (also known as Shang Gao's theorem, Pythagorean theorem) is a basic geometric theorem that was discovered by Shang Gao as early as the Shang Dynasty in China. It is said that after Pythagoras discovered this theorem, he beheaded a hundred cows in celebration, hence the "Hundred Oxen Theorem". The Pythagorean theorem states:

The sum of squares of the two right-angled sides of a right-angled triangle (i.e., the "hook" and "strand" for the short one is the hook and the long one is the strand) is equal to the square of the side length of the hypotenuse (i.e., the "string"). That is to say, if the two right-angled sides of a right-angled triangle are a and b, and the hypotenuse is c, then a 2 + b 2 = c 2 The Pythagorean theorem has found about 400 ways to prove it, which is one of the theorems with the most ways to prove in mathematics. The Pythagorean theorem is actually a special form of the cosine theorem.

Shang Gao, a famous mathematician in ancient China, said: "If the hook is three, the strand is four, then the string is five." It is recorded in the Nine Chapters of Arithmetic. ”

Let the side length of the square be x

Then the area of the large right triangle = (1 2) (a+x) (b+x) and because the large right triangle = the area of 2 pairs of small right triangles + the area of the square = 2 (1 2) ax + 2 (1 2) bx + x = ax + bx + x

1 2) (a+x) (b+x)=ax+bx+x multiplication of 2 on both sides yields: ab+ax+bx+x =2ax+2bx+2x then ab=ax+bx+x

a=3，b=5

ax+bx+x²=15

That is: the area of a large right triangle = 15

s distance = 2 15 = 30

The origin of the Pythagorean theorem: The Pythagorean theorem is also called the Pythagorean theorem, which is called the Pythagorean theorem in the West In ancient China, the shorter right-angled side in the right-angled triangle was called the hook, the longer right-angled side was called the strand, and the hypotenuse was called the string As early as more than 3,000 years ago, the Zhou Dynasty mathematician Shang Gao put forward the Pythagorean theorem in the form of "Hook three, strand four, string five", and later people further discovered and proved that the three-sided relationship of the right triangle is: the sum of the squares of the two right-angled sides is equal to the square of the hypotenuse.

In a right-angled triangle, two right-angled edges are known to find the acute angle, and the tangent is used, tan small angle = 1090 2270, small angle , large angle , hypotenuse = (1090 2 + 2270 2) 2518, tan small angle = 1090 2160, small angle , large angle , hypotenuse = (1090 2 + 2160 2) 2419.

In China, the sum of the squares of the two right-angled sides of a right-angled triangle is equal to the square of the hypotenuse is called the Pythagorean theorem or the Pythagorean theorem, also known as the Pythagorean theorem or Pythagoras theorem. is a fundamental geometric theorem that is traditionally believed to have been proved by Pythagoras in ancient Greece. It is said that after Pythagoras proved this theorem, he beheaded a hundred oxen in celebration, hence the "Hundred Oxen Theorem".

In China, a special case of the Pythagorean theorem is recorded in the Zhou Sutra, which is said to have been discovered by Shang Gao in the Shang Dynasty, so it is also called Shang Gao's theorem; Zhao Shuang of the Three Kingdoms period made a detailed annotation of the Pythagorean theorem in the "Zhou Ji Sutra" as a proof. France and Belgium call it the donkey bridge theorem, and Egypt calls it the Egyptian triangle. In ancient China, the shorter right-angled side of the right-angled triangle was called the hook, the longer right-angled side was called the strand, and the hypotenuse was called the chord.

Is this question difficult? I'll tell you the idea.

ab=6,bc=8,∴ac=10

cf=cd=6,∴af=4

Let de=ef=x, then ae=8-x, and rt aef is understood by the pythagorean determination x=3s cde=9, and the area of the rectangle minus one is trapezoidal.

What's so hard about this question? There are no questions that can't be done, only people who are too lazy to think.

The length of the natural droop of the bunting is actually the length of the point in the upper left corner of the diagram to the point in the lower right corner, that is, the length of the diagonal, which can be found using the Pythagorean theorem.

1 All Pythagorean theorem.

is a + b = c (a and b are the two right-angled sides of a right-angled triangle, and c is the hypotenuse of a right-angled triangle).

Then hook three strands, four strings, five.

Fine] [Rui] Huandong.