29. A path of uniform width runs round
the inside of a rectangular field 38
m long and 32 m wide. If the path
occupies 600 m², then the width
of the path is :
[SSC, 2007]
(a) 3 m
(b) 5 m
(c) 8.75 m (d) 10 m
Answers
Step-by-step explanation:
Description for Correct answer:
area of path =(l+b−2x)2x=600=(l+b−2x)2x=600
take help from options to save your valuable time take option (b) x = 5m
(38+32+2×5)2×5(38+32+2×5)2×5
=(70−10)×10=60×10=600
Step-by-step explanation:
Given :-
A path of uniform width runs round the inside of a rectangular field 38 m long and 32 m wide. If the path occupies 600 m².
To find:-
Find the width of the path?
Solution:-
Given that
Length of a rectangular field =(l) = 38 m
Breadth of the rectangular field =(b) = 32 m
We know that
Area of a rectangle = lb sq.units
Area of the rectangular field = 38×32 m²
= 1216 m²
Let the width of the path be w m
If it runs inside of the rectangular field then
Length of the inner rectangle = l-2w
=> 38-2w m
Breadth of the inner rectangle = b-2w
=> 32-2w m
Area of the inner rectangular field
=> (38-2w)×(32-2w)
=> 1216-76w-64w+4w²
=> (4w²-140w+1216 ) sq.m
Area of the path = Area of the outer rectangle - Area of the inner rectangle
=> 1216-(4w²-140w+1216)
=> 1216-4w²+140w-1216
=> -4w²+140w sq.m
According to the given problem
Area of the path = 600 m²
=> -4w²+140w = 600
=> -4w²+140w-600 = 0
=>-4(w²-35w+150) = 0
=> w²-35w+150 = 0/-4
=>w²-35w+150 = 0
=> w²+5w-30w+150 = 0
=> w(w-5)-30(w-5) = 0
=> (w-5)(w-30) = 0
=>w-5 = 0 or w-30 = 0
=> w = 5 or w = 30
w can not be equal to 30
Therefore, w = 5 m
Answer:-
The width of the path of the given rectangular field is 5m
Used formulae:-
Area of a rectangle whose length is l units and breadth is b units is lb sq.units