NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 6: Triangles - Exercise 6.1

Question 2

Step 1: A rhombus has diagonals that cut each other at right angles (90°) and also bisect each other (divide each other into two equal parts).

Step 2: The given diagonals are 16 cm and 12 cm.

Step 3: When they are bisected, each half of the diagonals will be:

• Half of 16 cm = 8 cm
• Half of 12 cm = 6 cm

Step 4: These halves form a right-angled triangle with the side of the rhombus as the hypotenuse.

Step 5: Using Pythagoras theorem: \( \text{(side)}^2 = (8)^2 + (6)^2 \) \( \text{(side)}^2 = 64 + 36 = 100 \) \( \text{side} = \sqrt{100} = 10 \; \text{cm} \)

Final Answer: The side length of the rhombus is 10 cm.