Question

Assertion: The diagonals of a rhombus are 6 cm and 8 cm. Its side is 10 cm.

Reason: The diagonals of a rhombus bisect each other at right angles.

Options

• Both A and R are true and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

A is false but R is true.

Explanation:

Assertion (A): The diagonals of a rhombus are 6 cm and 8 cm. Its side is 10 cm. 

In a rhombus, the diagonals bisect each other at right angles, forming four right-angled triangles.

Half of the diagonals are:

`6/2 = 3  cm` and `8/2 = 4  cm`

Using the Pythagoras theorem to find the side:

Side = `sqrt(3^2 + 4^2)`

= `sqrt(9 + 16)`

= `sqrt(25)`

= 5 cm

So, the side is 5 cm, not 10 cm.

Assertion is false.

Reason (R): The diagonals of a rhombus bisect each other at right angles.

This is a true geometric property of a rhombus.

Thus, A is false but R is true.