Question

the perimeter of rhombus is 100 cm and one of its shorter diagonal is 30 cm long find the length of other diagonal and area of Rhombus

Answer 1

Hope you understand my friend!!!

Answer 2

Answer:

Let OPQRS be a rhombus

Given ,

Perimeter of the rhombus = 100 cm

Diagonal (d1) = 30cm

Other Diagonal (d2) = ?

Area of the rhombus = ?

Perimeter of the rhombus= 4×side of the rhombus

= 100 = 4s

= s = 25

Let d1 = Diagonal = QS = 30 cm

= QO = QS/2 = 30/2 = 15 cm ( Diagonal bisect each other at right angle )

Now , let us find the second diagonal of the rhombus

In right - angled triangle QOR using Pythagoras Theorem ,

QR² = QO² + OR²

= 25² = 15² + OR²

= OR² = 625 - 225 = 400

Therefore , OR = /400 = 20 cm

= PR = 2×OR = 2×20 = 40 cm (Diagonal bisect each other)

Let PR = d2 , Hence , area of a rhombus

= 1/2 × d1 × d2

= (1/2 × 30 × 40 ) cm²

= (1/2 × 1200) cm²

= 600 cm²

Hence , The area of the rhombus = 600 cm²