Rohan bought a rhombus shaped field , whose diagonals are 2400 m and 1000 m. Rohan wants to fence it but don't know the length of its boundary. (a) Which of the following is the length of side of field ?
Answers
Answer:
Length of each side = 1300 m
Perimeter of field = 5200 m
Step-by-step explanation:
Use image given below as reference.
We know that diagonals of a rhombus perpendicularly bisect each other.
Now, let AC = 2400 m
Let BD = 1000 m
As AC and BD bisect each other,
DO = OB = 1000/2 = 500 m
AO = OC = 2400/2 = 1200 m
Now let's take a random triangle, like triangle DAO.
Applying Pythagoras' theorem, DO² + AO² = DA²
=> 500² + 1200² = DA²
=> 250000 + 1440000 = DA²
=> 1690000 = DA²
∴ DA = √1690000 => 1300 m is the length of each side of the field.
∴ Perimeter of rhombus = 4a = 4*1300 => 5200 m is the perimeter of field.
Perimeter of a rhombus with only diagonal given can also be found out by this formula --> 2√D1² + D2² where D1 and D2 are the 2 diagonals.
I didn't calculate the answer with formula directly as I had to make you understand the concept.
