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25 Jan 2021, 08:45
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Difficulty:
55%
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Question Stats:
59% (02:24) correct
41%
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The rectangular field is 14m long and 10m wide. There is a path of uniform width all around it, giving an area of 112 sq.m. What is the width of the path?
A. 1m
B. 2m
C. 4m
D. 6m
E. 8m
A. 1m
B. 2m
C. 4m
D. 6m
E. 8m
siddhantmittal
25 Jan 2021, 09:02
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We know that area of rectangle is length x breadth
Approach 1:
Start with option (c).. we know that if width of the track is 4m (and since it is a uniform track)
Area of park \(= 14*10 = 140 m^2\)
New length \(= 14 + 4 + 4 = 22m\)
New breadth \(= 10 + 4 + 4 = 18m\)
Area of path \(= (22*18 ) - (140) m ^2\)
Since this will give us 6 in the units place, we can rule out this option
If we plug in the value of option (b), we see that the difference of area matches with the area of path given
Hence the answer
Approach 2:
Consider the width of the track as x
New length \(= 14 + 2x\)
New breadth \(= 10 + 2x\)
Area of path\( = 112 = (14 + 2x)*(10+ 2x) - 140\)
Solve the quadratic to obtain the answer
Approach 1:
Start with option (c).. we know that if width of the track is 4m (and since it is a uniform track)
Area of park \(= 14*10 = 140 m^2\)
New length \(= 14 + 4 + 4 = 22m\)
New breadth \(= 10 + 4 + 4 = 18m\)
Area of path \(= (22*18 ) - (140) m ^2\)
Since this will give us 6 in the units place, we can rule out this option
If we plug in the value of option (b), we see that the difference of area matches with the area of path given
Hence the answer
Approach 2:
Consider the width of the track as x
New length \(= 14 + 2x\)
New breadth \(= 10 + 2x\)
Area of path\( = 112 = (14 + 2x)*(10+ 2x) - 140\)
Solve the quadratic to obtain the answer
ravigupta2912
25 Jan 2021, 10:27
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Let the uniform width be x, then
(14+2x)(10+2x) - 140 = 112
(14+2x)(10+2x) = 252
252 is the product of 2 integers with a difference of 4. Its easy to find the answer by hit and trial from here on.
2x = 4. Hence, x = 2
(14+2x)(10+2x) - 140 = 112
(14+2x)(10+2x) = 252
252 is the product of 2 integers with a difference of 4. Its easy to find the answer by hit and trial from here on.
2x = 4. Hence, x = 2
