If the area of rhombus is 96cm² and one of its diagonals is 12cm long,find the length of the other diagonal. Also, find its perimeter
Answers
Answer: 16cm and 40cm respectively
Step-by-step explanation:
Area of rhombus = d¹ × d² /2
96cm² = 12cm× d²cm /2
192cm² = 12d² cm²
d² = 16
2nd diagonal = 16 cm
The diagonals bisect one another divides the rhombus into four right angle triangles.
Picking one triangle..
One side will be half of one diagonal and another side the half of the 2nd diagonal leaving the third side which is the hypotenuse.
Hypotenuse ² = 8² + 6² = 64+36 =100
Hypotenuse = 10cm =length of one side
Perimeter = 4 × length
= 4 ×10 =40cm
Solution:-
• given:-
1)The area of rhombus is 96cm square .
2) one diagonal is 12 cm.
we know all side of rhombus are equal.
let, ac = 1st diagonal = 12 cm and
bd = 2cd diagonal ,
A = Area = 96cm.
=> Area of rhombus = [ac×bd]/2
=> A = [ac×bd]/2
=> 96 = [ 12 × bd ]/2
=> 96×2 = 12 × bd
=> 192 = 12 × bd
=> bd = 192/12
=> bd = 16 cm
•we know,
ac = ao + oc and bd = bo + od
• diagonals of a rhombus bisect each other at an angle of 90° or right angle.
means ao = oc = 12/2 = 6 cm &
bo = od = 16/2 = 8 cm.
in Δ aod
by Pythagoras theorem
=> (ad)² = (ao)² + (od) ²
=> (ad)² = (6)² + (8) ²
=> (ad)² = 36 + 64
=> (ad)² = 100
=> ad = √100
=> ad = 10 cm
•Perimeter of rhombus = 4 × sides
•Perimeter of rhombus = 4 × 10
•Perimeter of rhombus = 40 cm
Hence all side of rhombus are 10 cm and perimeter of rhombus is 40 cm
i hope it helps you .
