Question

Aryan wants to plant a flower on the ground in the form of a rhombus. The diagonals of the rhombus measures 42 cm and 56 cm. Find the perimeter of the field. (a) 150 cm (b) 140 cm (c) 130cm (d) 120cm​

Answer 1

Given info:-

Aryan wants to plant a flower on the ground in the form of a rhombus.The diagonals of the rhombus measures 42 cm and 56 cm.

Find the perimeter of the field ?

Explanation:-

Given that

rhombus.The diagonals of the rhombus measures 42 cm and 56 cm.

Let consider a rhombus ABCD

Let AC = (d1) = 42 cm

Let BD = (d2) = 56 cm

We know that

The digonals of a rhombus bisects each other at 90°.

AC = AO+OC

⇛ AC = 2 AO = 2 OC

⇛ AO = OC = AC/2

⇛ AO = OC = 42/2 = 21 cm

and

BD = BO+OD

⇛ BD = 2 BO = 2 OD

⇛ BO = OD = BD/2

⇛ BO = OD = 56/2 = 28 cm

We have,

∆AOB is a right angled triangle

By Pythagoras theorem,

AB² = AO²+OB²

⇛ AB² = 21²+28²

⇛ AB² = 441+784

⇛ AB² = 1225

⇛ AB = ±√1225

⇛ AB = ±35

AB is the length of the side which cannot be negative.

AB = 35 cm

We know that

All sides are equal in a rhombus

⇛ AB = BC = CD = DA

As we know

The Perimeter of a rhombus = 4×Side units

The perimeter of the rhombus ABCD

⇛ 4AB = 4BC = 4CD = 4DA

⇛ 4×35 cm

⇛ Perimeter = 140 cm

∴ The perimeter of the given field is 140 cm.