The length of AB is

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The length of AB is

The length of AB is

Answer :

 

Length is 9cm. The length of AB can be determined using the Pythagorean theorem. The sides 9, 12, and 15 are triples of 3, 4, 5 Pythagorean triples.

Detailed discussion of Length in Right Triangles

Pytahoras theorem or theorem Pythagoras is a theorem on a triangle a right angle where the sum of the two sides of a triangle is equal to the square of the length of the hypotenuse or the hypotenuse.

For triangle ABC right angled at B then apply

  • AB and BC are the sides of triangle ABC.
  • AC as the slanted side or hypotenuse.
  • Applies equality
    AB^2 \\:+\\: BC^2 \\:=\\: AC^2
    or
    AB^2 \\:=\\: AC^2 \\:-\\: BC^2
    or
    BC^2 \\:=\\: AC^2 \\:-\\: AC^2

In a right triangle, the hypotenuse is the longest side when compared to the lengths of the other sides. The three numbers that conform to the Pythagorean theorem are called Pythagorean triples. An example of a Pythagorean triple is:

  • 3, 4, and 5 and their multiples.
  • 5, 12, and 13 and their multiples.

Explanation with steps:

Is known:

  • Triangle ABC is right at B.
  • BC = 12 cm
  • AC = 15 cm

Asked:

  • AB?

Answer:

AB^2 \\:+\\: BC^2 \\:=\\: AC^2

AB^2 \\:+\\: 12^2 \\:=\\: 15^2

AB^2 \\:+\\: 144 \\:=\\: 225

AB^2 \\:=\\: 225 \\:-\\: 144

AB^2 \\:=\\: 81
AB \\:=\\: \\sqrt{81}

        = 9 cm

 

Question Details

Class : VIII

Course : Mathematics

Chapter : Pythagorean theorem

 

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