A charity trust decides to build a prayer hall having a carpet f 300 sq m with its length one metre more than twice its breadth. Find the length and breadth of the hall. What values do the students imbibe from the charity trust?
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Let l be the length and b be the breadth of the carpet
So, acc. to ques.
l+1=2b
l=2b-1
Now,
Since area of carpet= l×b
So,
300=l×b
300=(2b-1)×b
300=2b^2-b
2b^2-b-300=0
(2b^2-25b)+(24b-300)=0
b(2b-25)+12(2b-25)=0
(b+12)(2b-25)=0
Breadth= 2b-25=0
b=25/2=12.5 m
and,
Therefore,
Length=2b-1= 2×12.5-1= 24 m
So, acc. to ques.
l+1=2b
l=2b-1
Now,
Since area of carpet= l×b
So,
300=l×b
300=(2b-1)×b
300=2b^2-b
2b^2-b-300=0
(2b^2-25b)+(24b-300)=0
b(2b-25)+12(2b-25)=0
(b+12)(2b-25)=0
Breadth= 2b-25=0
b=25/2=12.5 m
and,
Therefore,
Length=2b-1= 2×12.5-1= 24 m
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