Area of any rhombus shaped all ground is 5400 square metre when rohan walks along the diagonal in the playground then distance covered by him is 120 find the distance cover is completing one rotation alongside of this field
Answers
The distance covered by completing one rotation alongside this field is 300 m.
Step-by-step explanation:
It is given that,
The area of the rhombus-shaped playground ABCD = 5400 m²
The distance covered by Rohan along the diagonal of the playground i.e., the length of the diagonal, AC = 120 m
Therefore,
The area of the rhombus-shaped playground = ½ * AC * BD
⇒ 5400 = ½ * 120 * BD
⇒ BD = 5400/60
⇒ BD = 90 m
We know that the diagonals of a rhombus bisect each other at 90 degrees.
∴ AO = ½ AC = ½ * 120 = 60 m
And
BO = ½ BD = ½ * 90 = 45 m
Now, considering the right triangle AOB and applying the Pythagoras theorem, we get
AB² = AO² + BO²
⇒ AB = √[60² + 45²]
⇒ AB = √[5625]
⇒ AB = 75 m
Thus,
The distance covered by Rohan while completing one rotation alongside the playground is given by,
= Perimeter of the rhombus-shaped playground
= AB + BC + CD + DA
= 75 + 75 + 75 + 75
= 300 m
-----------------------------------------------------------------------------------------------
Also View:
The area of playground is 4800m square .find the cost of covering it with gravel 1 cm deep,if the gravel costs Rs.4.80 per cubic meter.
https://brainly.in/question/1721018
A playground is in the town is in the form of a kite. the perimeter is 106 m. if one of its side is 23 cm. what are the length of other three sides ?
https://brainly.in/question/1564448
The area of rhombus 48m square,if one of its diagonal is 16 m , find the length of other diagonal ?
https://brainly.in/question/7127211
