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.
