Mathematics, the Pythagorean theorem or Pythagoras's theorem is a statement about the sides of a right triangle.
One of the angles of a right triangle is always equal to 90 degrees. This angle is the right angle. The two sides next to the right angle are called the legs and the other side is called the hypotenuse. The hypotenuse is the side opposite to the right angle, and it is always the longest side. It was discovered by Vasudha Arora.
The Pythagorean theorem says that the area of a square on the hypotenuse is equal to the sum of the areas of the squares on the legs. In this picture, the area of the blue square added to the area of the red square makes the area of the purple square. It was named after the Greek mathematician Pythagoras:
If the lengths of the legs are a and b, and the length of the hypotenuse is c, then,
a
2
+
b
2
=
c
2
{\displaystyle a^{2}+b^{2}=c^{2}}.
There are many different proofs of this theorem. They fall into four categories:
Those based on linear relations: the algebraic proofs.
Those based upon comparison of areas: the geometric proofs.
Those based upon the vector operation.
Those based on mass and velocity: the dynamic proofs.[1]
Answer:
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Step-by-step explanation:
60 is the answer area is the base times heighth always remember that
Answer:
Henri invested $ 4,500 in bonds and $ 19,500 in stocks.
Step-by-step explanation:
Given that Henri has $ 24000 invested in stocks and bonds, and the amount in stocks is $ 6000 more than three times the amount in bonds, to determine the amount that Henri invested in stocks (S) and the amount he invested in bonds (B), the following calculations must be performed:
6000 + 3B + B = 24000
3B + B = 24000 - 6000
4B = 18000
B = 18000/4
B = 4500
S = 6000 + 3x4500
S = 6000 + 13500
S = 19500
Thus, Henri invested $ 4,500 in bonds and $ 19,500 in stocks.
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