The area of a rhombus 96cm. If one of its diagonal is 16cm then find the length of its sides
Answers
Answer:
The answer is 10 cm
Step-by-step explanation:
The explanation is in attachment.
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Solution:-
• given:-
1)The area of rhombus is 96cm square .
2) one diagonal is 16 cm.
we know all side of rhombus are equal.
let, bd = 1st diagonal = 16 cm and
ac = 2cd diagonal ,
A = Area = 96cm.
=> Area of rhombus = [ac×bd]/2
=> A = [ac×bd]/2
=> 96 = [ ac × 16 ]/2
=> 96×2 = ac × 16
=> 192 = ac × 16
=> bd = 192/16
=> bd = 12 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
Hence all side of rhombus are
10 cm.
i hope it helps you.
