Question

the perimeter of a rhombus is 100 cm one of its diagonal is 40 cm find the length of the Other diagonal​

Answer 1

here your answer i hope you will understand

Answer 2

$\huge\sf{\underline{\underline{Solution:}}}$

Perimeter of Rhombus: 100 cm

Rhombus has 4 equal sides.

Therefore,

the length of each side is:  100 / 4 = 25 cm

Therefore length of each side of rhombus is 25 cm.

Also, the diagonals of a rhombus bisect each other at a point. In our case, the point is called O. We are given that, AC = 40 cm.

Therefore OA = 40 / 2 = 20 cm

Now consider Δ AOB.

By Pythagoras Theorem we get,

⇒ OA² + OB² = AB²

⇒ 20² + OB² = 25²

⇒ OB² = 25² - 20²

⇒ OB² = 625 - 400

⇒ OB² = 225

⇒ OB = √ 225 = 15 units.

Now we need the length of BD. We know that OB is half of BD.

Therefore BD = 2 × 15 = 30 units

Therefore the length of other diagonal is 30 cm.