area of a rectangular field whose length is twice its breadth is 4050 cm square A man cycles along the boundary of field at 45 cm per second find the time taken by him to return to the starting point
Answers
Let the breadth of the rectangle be x.
The length is 2x.
The area of a rectangle = Length × Width
The area = 2x × x = 2x²
This equals to 4050.
Equating the two we have :
2x² = 4050
x² = 4050/2
x² = 2025
x = √2025
x = 45 cm
The length is thus 45 × 2 = 90cm
When the man cycles around, he covers the perimeter of the field.
Perimeter = 2(W + L)
Perimeter = 2(90 + 45) = 2 × 135 = 270cm
Now :
Distance = 270 cm
Speed = 45 cm per second
Time = Distance / Speed
= 270/45 = 6
We have 6 seconds
The breath of the rectangular field is B and the length is 2B
Area of the rectangular field = 4050 square cm
L * B = 4050
2B * B = 4050
B^2 = 4050/2 = 2025
B = square root of 2025 = 45 cm
Hence L = 2 * B = 2 * 45 = 90 cm
Speed of the cycle = 45 cm/sec
Perimeter of the field = 2 (L + B) = 2 (45 + 90) = 270 cm
Speed = distance/time
Time = distance/speed
Time = 270/45
Time = 6 sec