Question

can someone explain me what is Pythagoras theorem in detail​

Answer 1

Answer:

Example 1 – The hypotenuse of a right triangle is 1 inch longer than the longer leg. The shorter leg is 7 inches shorter than the longer leg. Find the length of the hypotenuse.

Step 1: Draw a right triangle and then read through the problems again to determine the length of the legs and the hypotenuse.

Step 1

Step 2: Use the Pythagorean Theorem (a2 + b2 = c2) to write an equation to be solved.

Step 2

Step 3: Simplify the equation by distributing and combining like terms as needed.

Step 3

Step 4: Solve the equation. In the case, we need to get the equation equal to zero and solve by factoring.

Step 4

Step 5: Answer the question asked in the original question and make sure that the answer makes sense. Do not forget to include units in your final answer. In this case, x = 4 does not make sense because 4 – 7 = –3 which is impossible, so x = 12 is the correct answer.

Step 5

Answer 2

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Pythagoras Theorem

Pythagoras Theorem is an important topic in Maths, which explains the relation between the sides of a right-angled triangle. It is also sometimes called the Pythagorean Theorem. The formula and proof of this theorem are explained here with examples.

Pythagoras theorem is basically used to find the length of an unknown side and angle of a triangle. By this theorem, we can derive base, perpendicular and hypotenuse formula.

Pythagoras Theorem Statement

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named as Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.

Pythagoras Theorem-Right Angle Triangle

History

The theorem is named after a greek Mathematician called Pythagoras.

Pythagoras Theorem Formula

Consider the triangle given above:

Where “a” is the perpendicular side,

“b” is the base,

“c” is the hypotenuse side.

According to the definition, the Pythagoras Theorem formula is given as:

Hypotenuse2 = Perpendicular2 + Base2

c2 = a2 + b2

The side opposite to the right angle (90°) is the longest side (known as Hypotenuse) because the side opposite to the greatest angle is the longest.

Pythagoras Theorem

Consider three squares of sides a, b, c mounted on the three sides of a triangle having the same sides as shown.

By Pythagoras Theorem –

Area of square A + Area of square B = Area of square C...

Applications of Pythagoras Theorem

To know if the triangle is a right-angled triangle or not.

In a right-angled triangle, we can calculate the length of any side if the other two sides are given.

To find the diagonal of a square.

Useful For

Pythagoras theorem is useful to find the sides of a right-angled triangle. If we know the two sides of a right triangle, then we can find the third side.

How to use?

To use this theorem, remember the formula given below:

c2 = a2 + b2

Where a, b and c are the sides of the right triangle.

For example, if the value of a = 3 cm, b = 4 cm, then find the value of c.

We know,

c2 = a2 + b2

c2 = 32+42

c2 = 9+16

c2 = 25

c = √25

c = 5

Hence, the third side is 5 cm.

As we can see, a + b > c

3 + 4 > 5

7 > 5

Hence, c = 5 cm is the hypotenuse of the given triangle....

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Hope it helps you :)