Question

Q.1 The length of the diagonals of a rhombus are 24 cm & 18 cm resp. Find the length of each side of the rhombus. (A) 15 cm (B) 18 cm (C) 20 cm (D) 22 cm​

Answer 1

Solution Tips

To solve this question, we must remember:

✳ The diagonals of a rhombus perpendicularly bisect each other. This property tell us that each diagonal will bisect the other at a right angle, so the rhombus is divided into four right-angled triangles.

✳ The Pythagoras Theorem will help us find the hypotenuse, which is the side of the rhombus, of the four right-angled triangles in our rhombus. It states that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the sides, which means:

$\boxed{\sf{s^{2}+s^{2}=h^{2}}}$

Answer:

Given:

• A rhombus
• Diagonals: 24 cm and 18 cm

To find:

• The length of the side

Solution:

Let us first name the rhombus ABCD and the point where the diagonals intersect O. (as in the attachment)

Taking ΔAOD

We know that:

• OD = 24/2 = 12 cm
• AO = 18/2 = 9 cm

Now, let us find the hypotenuse, side AD, using the Pythagoras Theorem. We know that:

⇒ OD² + AO² = AD²

⇒ 12² + 9² = AD²

⇒ 144 + 81 = AD²

⇒ 225 = AD²

⇒ AD = √225

⇒ AD = 15 cm

Therefore, the length of each side of the rhombus is (A) 15 cm.