Bissoy.com
Doctors Medicines MCQs Q&A

A rectangular wheat field has an area of 1682 sq. metres whereas its perimeter is 29a × 3b × 2c metres. If the length and breadth are positive integers, then find the perimeter. (It is known that a, b, c are positive integers.)

A rectangular wheat field has an area of 1682 sq. metres whereas its perimeter is 29a × 3b × 2c metres. If the length and breadth are positive integers, then find the perimeter. (It is known that a, b, c are positive integers.) Correct Answer 174 metres

Given:

Area = 1682 sq. metres

Perimeter =  29a × 3b × 2c metres (a, b, c are positive integers)

Calculation:

The expression for the perimeter shows that the perimeter has the factors 29, 3, and 2 to some powers a, b, and c respectively.

So, let us factoise the options:

174 = 2 × 3 × 29

58 = 2 × 29 

116 = 2 × 2 × 29

87 = 3 × 29

From the above, we can see that only option 1 has all three as its factors.

∴ The perimeter of the field is 174 m.

Note: The value of a, b, and c in the expression is said to be positive integers. So, the minimum value of a, b, and c is 1. 

Related Questions

The perimeter of a rectangular field is fourth times of the perimeter of a square field. The ratio of the length of the rectangular field to the side of the square field is 6:1 and the diagonal of the square is 5√2 cm. Then, the area of the square field is what percentage of the area of the rectangular field?
The area of a circular field is equal to the area of a rectangular field. The ratio of the length and the breadth of the rectangular field is 14 : 11 respectively and perimeter is 100 metres. What is the diameter of the circular field ?
The length of a rectangular blackboard is 8 m more than its breadth. If its length is increased by 7 m and its breadth is decreased by 4 m, its area remains unchanged. The length and breadth of the rectangular blackboard is :
The breadth of a rectangular field is $$\frac{3}{4}$$ of its length and its area is 300 sq. metres. What will be the area (in sq. metres) of the garden of breath 1.5 metres developed around the field ?
The perimeter of a circular park is equal to the perimeter of a rectangular field. If the ratio of the length and breadth of the rectangular field is 3 ∶ 1 and the area of it is 363 m2, then what will be the area of the circular park?
The length of a rectangular field is equal to the 8√2 times the diagonal of a square, whose area is 64 m2. The ratio of length and breadth of the rectangular field is 2 : 1 respectively. Find the cost of paving the rectangular field at the rate of Rs. 0.50 per m2.
The length and breadth of a rectangular field is in the ratio of 4 : 3 and the area of the rectangular field is 192 cm2. A contractor took the contract of watering the whole field at Rs. 12 / cm2. Find the perimeter of the rectangle and also find the total cost of watering.
The length of rope required for fencing the rectangular field is 98 m. The length and breadth of the rectangular field is consecutive number. What is the area of the rectangular field?
A rectangular field has 4 cm length and 3 cm width. From the corner of this field, a small square of side 1 cm is cut off. What will be the ratio of the length of the boundary of the rectangular field before cutting square and length of the boundary of the rectangular field after cutting square?  
The length and breadth of a rectangular field are in the ratio of 6 : 5. If the perimeter of the field is 132 metres, then what is its breadth?