Question

what is Pythagores explain it ​

Answer 1

Question:

• What is Phythagoras Theorem?

Explanation:

Pythagoras Theorem is an important topic in maths, which explain the relation between the sides of a right-angled triangle. It is also sometimes called the Pythagorean Theorem.

$\tt\color{teal}{†\:Uses\:of\:Pythagoras\:Theorem}$

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. Let's find out clearly.

$\tt\color{teal}{†\:Statment\:of\:Pythagoras\:Theorem:}$

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.

$\tt\color{teal}{†\:Pythagoras\:Theorem\: formula:}$

Consider the triangle given above(diagram 1st)

Where “a” is the perpendicular,

“b” is the base,

“c” is the hypotenuse.

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

$\underline{\boxed{ \sf Hypotenuse² = Perpendicular² + Base²}}\small\color{lime}{★}$

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.

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”

$\tt\color{teal}{†\:Example:}$

Consider a right triangle, given above (Attachment 2nd)

Find:

• The value of x.

Solution:

X is the side opposite to right angle,

Hence it is a hypotenuse.

Now, by the theorem we know;

$\underline{\boxed{ \sf Hypotenuse² = Perpendicular² + Base²}}\small\color{lime}{★}$

⤏x²= 8² + 6²

⤏x² = 64+36 = 100

⤏x = √100 = 10

Therefore, the value of x is 10.

────────────────────