The lengths of the diagonals of a rhombus are 16 cm and 12 cm. Then, the length of the side of the rhombus is
a. 9 cm
b. 10 cm
c. 8 cm
d. 20 cm

Solution:

Given, the length of the diagonals of a rhombus are 16 cm and 12 cm.

We have to find the length of the side of the rhombus.

A rhombus is a quadrilateral whose four sides all have the same length.

Let us consider a rhombus ABCD

The diagonals are AC = d₁ =16 cm and BD = d₂ = 12 cm intersect at a point O.

So, AO = AC/2 = 16/2 = 8 cm

BO = 12/2 = 6 cm

Consider the right triangle AOB,

By using Pythagorean theorem,

AB² = AO² + BO²

AB² = (8)² + (6)²

AB² = 64 + 36

AB² = 100

Taking square root,

AB = 10 cm

Therefore, the length of the side of the rhombus is 10 cm.

✦ Try This: The lengths of the diagonals of a rhombus are 12 cm and 18 cm. Then, the length of the side of the rhombus is

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6

NCERT Exemplar Class 10 Maths Exercise 6.1 Problem 2

The lengths of the diagonals of a rhombus are 16 cm and 12 cm. Then, the length of the side of the rhombus is, a. 9 cm, b. 10 cm, c. 8 cm, d. 20 cm

Summary:

The lengths of the diagonals of a rhombus are 16 cm and 12 cm. Then, the length of the side of the rhombus is 10 cm

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