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PQID: PS98502.01 | OG 2020: Question No. 98

Three-fourths of the area of a rectangular lawn 30 feet wide by 40 feet long is to be enclosed by a rectangular fence. If the enclosure has full width and reduced length rather than full length and reduced width, how much less fence will be needed?

1. 2(1/2)
2. 5
3. 10
4. 15
5. 20

Source	OG 2020
PQID	PS98502.01
Type	Problem Solving
Topic	Geometry
Sub-Topic	Polygon
Difficulty	Hard

Solution

Given

In this question, we are given

• A rectangular lawn is 30 feet wide and 40 feet long.
• Three-fourth of the area of the lawn is to be enclosed by a rectangular fence.

To Find

We need to determine

• The less amount of fence required, if the enclosure has full width and reduced length, compared to full length and reduced width.

Approach & Working

• Area of lawn = 30 × 40
  • 3/4^th of the area of lawn = ¾(30 × 40) = 30 * 30

Case 1: When full width will be fenced, and reduced length will be fenced.

• Width = 30 feet
  • 30 * L = 30 * 30
• Hence, length = 30 feet
• Length of fence needed = 2(30 + 30) = 120 feet

Case 2: When full length will be fenced, and reduced width will be fenced

• Length = 40 feet
  • 40 * W = 30 * 30
    • W = 22.5 feet
  • Length of fence needed = 2(40 + 22.5) = 125 feet

Difference in length of fence needed = 125 – 120 = 5 feet.

Hence, option B is the correct answer.

Takeaways:

1. For the same area, the perimeter of a rectangle could be different depending on the length and breadth of the rectangle.
2. When the area of a rectangle and the length of one of the sides is known, the length of the other side can be determined as (Area of the rectangle/length of one side).