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Pythagoras Theorem:
The mathematical statement states that “In a rightangled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”
According to the Pythagoras theorem, if we have a triangle ABC, which is rightangled at B such that ab is equal to length and bc is equal to breadth, then the side CA is the hypotenuse which is equal to the sum of (ab)’s square and (bc)’s square.
The side ab is also known as perpendicular/ height, bc is known as base, and ac is known as the hypotenuse of the rightangled triangle ABC, where angle B= 90degree.
Also, the hypotenuse is the longest side in a rightangled triangle.
Greek Mathematician called Pythagoras found out this theorem hence the name is the same as his own name.
The formula:
(perpendicular)^2 +(base)^2= (hypotenuse)^2
Uses of Pythagoras Theorem:
1. To identify the triangle as a rightangled triangle.
2. Any unknown side can be calculated
3. To calculate the length of the hypotenuse.
Examples:
1. The two sides of a rightangled triangle are 10cm and 15cm. Find the third side which is the longest side.
So lets consider ABC, wher angle B = 90 degree
AB= 10cm
BC= 15cm
Hence by pythaogras theorem,
(AB)^2 +(BC)^2= (AC)^2
Now, putting the values,
or, 10^2 + 15^2 = (AC)^2
or, (AC)^2 = 100+225
or, AC = √325
or, AC = 18.02
Hence, AC is equal to 18.02. So the length of the longest side is 18.02cm
2. The height and hypotenuse of a rightangled triangle are 20cm and 25cm respectively. What is the length of the base?
So again let us consider ABC, where angle B = 90 degree
AB= 20cm
AC= 25cm
Hence by Pythagoras theorem,
(AB)^2 +(BC)^2= (AC)^2
Now, putting the values,
or, 20^2 + (BC)^2 = 25^2
or, (BC)^2 = 625400
or BC = √225
or, BC = 15
Hence, BC is equal to 15. So the length of the 15cm