find the perimeter of the question
Answers
Answer:
Perimeter of Rhombus= 4a
Therefore, a=√p²+q²
2
P= 2√p²+q²
= 2•√56²+42²
= 140cm
Therefore perimeter of field is 140cm
Step-by-step explanation:
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Option (b)
Step-by-step explanation:
Given :-
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.
To find :-
Find the perimeter of the field ?
Solution :-
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
Answer :-
The perimeter of the given field is 140 cm
Used Properties:-
→ The digonals of a rhombus bisects each other at 90°.
→All sides are equal in a rhombus
Used formulae :-
→The Perimeter of a rhombus = 4×Side units
Used Theorem :-
Pythagoras Theorem:-
" In a right angled triangle, The square of the hypotenuse is equal to the sum of the squares of the other two sides ".
