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13 Feb 2023, 23:55
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C
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Difficulty:
45%
(medium)
Question Stats:
68% (02:59) correct
32%
(02:52)
wrong
based on 78
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A path around the lawn has a constant width. The area of the path is 132 square yards. The perimeter of the lawn is 32 yards. What is the width of the path in yards ?
A. 1
B. 2
C. 3
D. 4
E. 5
Attachment:
2023-02-14_10-52-11.png [ 2.88 KiB | Viewed 2804 times ]
08 Mar 2023, 03:20
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Let x and y be the sides of the lawn
Perimeter of lawn is 32 yards
Therefore 2(x+y) = 32
x + y = 32
Let z be the width of the lawn
Length of rectangle (Lawn + path) = x + 2z
Breadth of rectangle (Lawn + path) = y + 2z
Now area of (Lawn + Path) - area of Lawn = area of path
(x + 2z)(y + 2z) - xy = 132 yards
Simplifying this we get 4z^2 + 32z = 132
4z^2 + 32z - 132 = 0
From this we get two solutions
z = - 11, 3
z can't be negative so z = 3
Option (C) is correct
Perimeter of lawn is 32 yards
Therefore 2(x+y) = 32
x + y = 32
Let z be the width of the lawn
Length of rectangle (Lawn + path) = x + 2z
Breadth of rectangle (Lawn + path) = y + 2z
Now area of (Lawn + Path) - area of Lawn = area of path
(x + 2z)(y + 2z) - xy = 132 yards
Simplifying this we get 4z^2 + 32z = 132
4z^2 + 32z - 132 = 0
From this we get two solutions
z = - 11, 3
z can't be negative so z = 3
Option (C) is correct
08 Mar 2023, 07:47
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My doubt is, it is nowhere mentioned that it is a rectangle, and we are also told to not trust diagrams unless explicitly stated. How can we assume here that the shape is rectangle?
