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?
- 2(1/2)
- 5
- 10
- 15
- 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 Ć 40
- 3/4th of the area of lawn = Ā¾(30 Ć 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
- 40 * W = 30 * 30
Difference in length of fence needed = 125 – 120 = 5 feet.
Hence, option B is the correct answer.
Takeaways:
- For the same area, the perimeter of a rectangle could be different depending on the length and breadth of the rectangle.
- 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).