Question
Here is the question : IF TWO LEGS OF A RIGHT TRIANGLE ARE 9 AND 12, WHAT IS THE HYPOTENUSE?
Option
Here is the option for the question :
- 2
- 11
- 15
- 21
The Answer:
And, the answer for the the question is :
Explanation:
The Pythagorean theorem, an equation that determines the lengths of the sides of a right triangle, can be applied to this geometry problem. A right triangle with legs A and B and a hypotenuse (the longest side) C has the formula a2 + b2 = c2 (2 means’squared’). When the leg variables are substituted into the equation, it becomes 92 + 122 = c2. Separate the variable by reducing the equation to its simplest form: 81 + 144 = c2, and then to 225 = c2. Finally, we get c = 15 by taking the square root of each side.
In geometry, a right triangle is a triangle that has one angle measuring 90 degrees. The side opposite the right angle is called the hypotenuse, while the other two sides are called the legs. The Pythagorean theorem is a fundamental formula that relates the lengths of the sides of a right triangle.
The given problem asks to find the length of the hypotenuse of a right triangle given the lengths of its two legs, which are 9 and 12. To solve this problem, we can use the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. In other words, if a and b are the lengths of the legs of a right triangle, and c is the length of the hypotenuse, then:
c^2 = a^2 + b^2
Substituting the values given in the problem, we get:
c^2 = 9^2 + 12^2
Simplifying the expression on the right-hand side, we get:
c^2 = 81 + 144
Combining like terms, we get:
c^2 = 225
Taking the square root of both sides of the equation, we get:
c = 15
Therefore, the length of the hypotenuse of the right triangle is 15.
The Pythagorean theorem is a fundamental formula in geometry and has many practical applications. It is used in various fields, such as engineering, physics, and architecture, to calculate distances, areas, and volumes. For example, in construction, the Pythagorean theorem is used to ensure that structures are built at right angles and to calculate the lengths of diagonal and inclined beams.
the Pythagorean theorem also has theoretical significance. It is one of the oldest and most well-known mathematical formulas, and it has been studied and generalized in many different ways. The Pythagorean theorem is a fundamental result in Euclidean geometry, which is the study of geometry based on a set of axioms first formulated by the ancient Greek mathematician Euclid.
The Pythagorean theorem also has cultural significance. It is named after the ancient Greek mathematician Pythagoras, who was one of the most influential figures in the history of mathematics and philosophy. Pythagoras and his followers believed that numbers and geometry were the key to understanding the universe, and they developed a rich and complex system of mathematics and philosophy based on these ideas.
the problem of finding the length of the hypotenuse of a right triangle given the lengths of its two legs is a fundamental application of the Pythagorean theorem. The Pythagorean theorem is a fundamental formula in geometry that relates the lengths of the sides of a right triangle. It has practical applications in various fields, and it is a fundamental result in Euclidean geometry. The Pythagorean theorem is also areflection of the cultural and philosophical beliefs of ancient Greek mathematicians, such as Pythagoras, who saw mathematics as a path to understanding the universe. Understanding the Pythagorean theorem and its ap