Question

Pythagoras theorem explanations

Answer 1

Hello friend
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It was the mathematician Pythagoras who first enunciated this important theorem about the right angled triangles.Hence ,it is called Pythagoras theorem.You know that the area of a square is (side)^2 Hence the Pythagoras theorem enunciated above can also be written as,

(Hypotenuse)^2 = (one side)^2 + (second sides)^2

Finding the hypotenuse from the sides containing the right angle.

Let's take an example,

Ex.1.) The length of the sides forming the right angle of a triangle angled triangle are 6 cm and 8 cm . Find the hypotenuse.

=) In the example

One side = 6 cm

another side = 8 cm.

hypotenuse = ?

According to the Pythagoras theorem

(Hypotenuse)^2 = (one side)^2 + (second sides)^2

By putting the given values we get,

(Hypotenuse )^2 = (6)^2 + (8)^2

(hypotenuse)^2 = 36 + 64

(hypotenuse)^2 = 100

hypotenuse = 10 cm. ........(taking square root)

By using the Pythagoras theorem you can find the another side in fact this theorem is also used in the physics while calculating the Displacement.

I hope this will helps you.

If you have any queries then please ask.

Thanks.

Answer 2

Hello Dear!

●Introduction
Buddhayan, an Indian Mathematician, developed a relationship between the squares described on the hypotenuse of a right-angled triangle and the sum of squares described on the remaining two sides of the triangle. However, the credit of the present form of this relationship goes to a Greek Mathematician Pythagoras and I known as Pythagoras Theorem.

●Statement of Pythagoras Theorem
In a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the remaining two sides.

●Equation of Pythagoras Theorem
If we let the hypotenuse of a right-angled triangle be 'h' and the remaining two sides be 'b' and 'p', then the equation will be as follows:
${h}^{2} = {p}^{2} + {b}^{2}$
Now to understand nicely, consider a triangle as given in the picture attached with this answer. It has three sides, namely, AB, BC, and AC. If we apply Pythagoras Theorem here then the equation will be,
${AC}^{2} = {AB}^{2} + {BC}^{2}$

➡I hope this explanation helps you!