The length of a rectangular field is 120 meters more than its breadth. The perimeter of the field is 760 meters.

Consider the following statements:

Statement I: The length of the field is 440 meters.
Statement II: The area of the field is 132,000 square meters.

Select the correct answer from below:

(a) Only Statement I is correct.
(b) Only Statement II is correct.
(c) Both statements I and II are correct.
(d) None of the statements is correct.

Question

The length of a rectangular field is 120 meters more than its breadth. The perimeter of the field is 760 meters.

Consider the following statements:

Statement I: The length of the field is 440 meters.
Statement II: The area of the field is 132,000 square meters.

Select the correct answer from below:

(a) Only Statement I is correct.
(b) Only Statement II is correct.
(c) Both statements I and II are correct.
(d) None of the statements is correct.

ONLiNE UPSC · Accepted Answer

The length of the rectangular field is 120 meters more than its breadth. The perimeter of the field is 760 meters.

Let the breadth of the field be x meters.
Then, the length of the field = x+120 meters.

Using the perimeter formula:

Perimeter=2(Length + Breadth) = 760m

2((x + 120) + x= 760 = 2(2 x+ 120) = 760

4x+240 = 760

x = 130

So, the breadth = 130 meters, and the length = 130 + 120 = 250 meters

Statement I: The length of the field is 440 meters.
We calculated the length as 250 meters, so Statement I is incorrect.

Statement II: The area of the field is 132,000 square meters.
The area of the field = Length &times; Breadth = 250 &times; 130 = 32,500&thinsp;m2

So, Statement II is incorrect.

Therefore, option (d) is correct.

Geometry

Rectangles

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