KnowledgeBoat Logo

Mathematics

If a side of a rhombus is 10 cm and one of the diagonals is 16 cm, then the length of the other diagonal is

  1. 6 cm

  2. 12 cm

  3. 20 cm

  4. 12 cm

Pythagoras Theorem

3 Likes

Answer

Let AC = 16 cm.

If a side of a rhombus is 10 cm and one of the diagonals is 16 cm, then the length of the other diagonal is? Pythagoras Theorem, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

We know that,

Diagonals of rhombus are perpendicular and bisect each other,

AO = 12\dfrac{1}{2}AC = 8 cm.

In right triangle AOB,

By pythagoras theorem we get,

⇒ AB2 = AO2 + OB2

⇒ 102 = 82 + OB2

⇒ 100 = 64 + OB2

⇒ OB2 = 100 - 64 = 36

⇒ OB = 36\sqrt{36} = 6 cm.

BD = 2OB = 12 cm.

Hence, Option 2 is the correct option.

Answered By

2 Likes

Related Questions