The length of a rectangular hall is 4 metres more than its breadth. If the perimeter of the hall is 56 metres, find its length and breadth.
Answers
Explanation:
Length \large\leadsto\boxed{\tt\purple{16 \: m}}⇝
16m
\red{\bigstar}★ Breadth \large\leadsto\boxed{\tt\purple{12 \: m}}⇝
12m
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• Given:-
Length of rectangular hall is 4m more than its breadth.
Perimeter of the hall is 56m.
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• To Find:-
Length and breadth of the rectangular hall.
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• Solution:-
Let the breadth of the rectangular hall be 'x'.
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Given that,
Length of the rectangular hall is 4 metres more than its breadth.
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Therefore,
Length of the rectangular hall is 'x+4'.
★ Figure:-
\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(2,3.5){\sf\large x+4 m}\put(-1.4,1.4){\sf\large x m}\put(2,1.4){\large\bf 56 m}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}
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We know,
\pink{\bigstar}★ \large\underline{\boxed{\bf\green{Perimeter = 2(l+b)}}}
Perimeter=2(l+b)
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➪ \sf 56 = 2((x+4) + x)56=2((x+4)+x)
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➪ \sf 56 = 2(x + 4 + x)56=2(x+4+x)
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➪ \sf 56 = 2(2x+4)56=2(2x+4)
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➪ \sf 56 = 4x + 856=4x+8
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➪ \sf 4x = 56 - 84x=56−8
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➪ \sf 4x = 484x=48
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➪ \sf x = \dfrac{48}{4}x=
4
48
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★ \large{\bf\pink{12}}12
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Hence,
Length = x + 4 → 12 + 4 → 16 m
Breadth = 12 m
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Therefore, the length and breadth of the rectangular hall is 16m and 12m respectively.
Ans. Let t be the duration of flight in hrs. and v be the corresponding speed.
Clearly t = 720/v…..(1)
t + 1/2 = 720/v - 250……(2)
Eliminate v from these equations we have
72/t = (144/2t +1) + 25
This becomes a quadratic equation
50t square + 25t - 72 = 0
t = (-25 +√625 + 4 × 50 × 72) /2×50
t =( -25 + √15025) /100
t = 0.976 hrs or 60×0.976 = 58.56min. Ans