Practice Math With Us

Pythagorean Theorem Squares

Pythagorean theorem is one of the basic fundamental theorem in mathematics. This theorem is suitable for a right angle triangle. Pythagorean theorem says with the length of a side squares of a right angle triangle. The name of a Pythagorean theorem is given by a mathematician Pythagoras, hence it is also called as Pythagoras theorem.


Please express your views of this topic  Pythagorean Theorem History by commenting on artile. 


Statement of Pythagorean theorem squares:


Statement of Pythagorean theorem squares is as follows.

The square of a hypotenuse area of a right angle triangle is obtained by addition of the squares of other two sides area of triangle. The other two sides are termed as opposite and adjacent side of a right angle triangle.

Representation of right angle triangle:

Squareofhypotenuseistheadditionofsquaresofothertwosides

Form the above figure the Pythagorean theorem is,

Hypotenuse area2 = Opposite area2 +  Adjacent area2


Example problems for Pythagorean theorem squares:


Example: 1

The opposite area of right angle triangle is 14 and the adjacent area of right angle is 15.Determine the hypotenuse of a right angle triangle.

Solution:

Given,

Opposite area of right angle triangle = 14 m

Adjacent area of right angle triangle = 15 m

Pythagorean theorem is ,

Hypotenuse area2 = Opposite area2 +  Adjacent area2

    = 142 + 152

    = 196 + 225.

    = 421

Hypotenuse  =`sqrt(421)` = 20.51 m

 

The hypotenuse of a given right angle triangle is 20.51 m.

Example: 2

       A right angle triangle has opposite side of 13 and hypotenuse side of 15. Find the adjacent side of ar ight angle triangle.

Solution:

Given,

Opposite side = 13 m

Hypotenuse side = 15

Hypotenuse area2 = Opposite area2 +  Adjacent area2

Adjacent area2 = Hypotenuse area2 - Opposite area2

= 152 - 132

= 225 - 169

= 56

= `sqrt(56)` = 7.48 m.

The adjacent side of a given right angle triangle is 7.48 m.


Between, if you have problem on these topics Angle of Elevation Formula , please browse expert math related websites for more help on  cbse vs state board. 


Practice problems for Pythagorean theorem squares:


Problem: 1

A right angle triangle has opposite side of 4 and adjacent  side area of 3.Determine the hypotenuse side area of a right angle triangle.

Answer: 5 m

Problem: 2

A right angle triangle has opposite side of 12 and adjacent  side area of 9. Determine the hypotenuse side area of a right angle triangle.

Answer: 15