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The ratio of perimeter of triangle to the perimeter of rectangle be

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The ratio of perimeter of triangle to the perimeter of rectangle be  [#permalink]

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New post 19 Feb 2020, 16:04
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The ratio of perimeter of triangle to the perimeter of rectangle be 2:1. Length of rectangle is 25% less than side of a square and ratio of length to breadth of rectangle is 3 : 2. If difference between perimeter of square and that of rectangle is 42 cm, then find perimeter of triangle?
(A) 120 cm
(B) 140 cm
(C) 121 cm
(D) 100 cm
(E) 96 cm

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Re: The ratio of perimeter of triangle to the perimeter of rectangle be  [#permalink]

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New post 19 Feb 2020, 22:13
TheNightKing wrote:
The ratio of perimeter of triangle to the perimeter of rectangle be 2:1. Length of rectangle is 25% less than side of a square and ratio of length to breadth of rectangle is 3 : 2. If difference between perimeter of square and that of rectangle is 42 cm, then find perimeter of triangle?
(A) 120 cm
(B) 140 cm
(C) 121 cm
(D) 100 cm
(E) 96 cm



Let the side of square be s, so length of rectangle will be 0.75s..
Now l:b=3:2, so b=0.75s*2/3=0.5s

Perimeter of square = 4s and that of rectangle = 2(0.75s+0.50s)=2.5s
Difference = 4s-2.5s=1.5s=42....s=28

Perimeter of rectangle = 2.5s=2.5*28=70
Perimeter of triangle = 2*P of rectangle = 2*70=140

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Re: The ratio of perimeter of triangle to the perimeter of rectangle be  [#permalink]

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New post 19 Feb 2020, 22:34
Tip: Write down the relations as u read the question.

ANS. : B

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Re: The ratio of perimeter of triangle to the perimeter of rectangle be  [#permalink]

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New post 19 Feb 2020, 23:03
TheNightKing wrote:
The ratio of perimeter of triangle to the perimeter of rectangle be 2:1. Length of rectangle is 25% less than side of a square and ratio of length to breadth of rectangle is 3 : 2. If difference between perimeter of square and that of rectangle is 42 cm, then find perimeter of triangle?
(A) 120 cm
(B) 140 cm
(C) 121 cm
(D) 100 cm
(E) 96 cm


Solution:


    • \(\frac{(Perimeter\ of\ triangle)}{(Perimeter\ of\ rectangle)}=\frac{2}{1}\)
      o \(Perimeter\ of\ triangle = 2*(Perimeter\ of\ rectangle)\)…(i)
    • Let a be the side of square
      o Perimeter of Square = \(4*a\)…(ii)
    • Length of the Rectangle = \(a – \frac{25}{100}*a = \frac{3}{4}*a\)
      o Breadth of rectangle = \(\frac{2}{3}*\frac{3}{4}*a=\frac{1}{2}*a\)
      o Perimeter of rectangle=\(2(\frac{3}{4}*a+\frac{1}{2}*a)=\frac{5}{2}*a\)…(iii)
    • Difference between the perimeter of square and rectangle = \(42\)CM
      o From equation (ii) and (iii)
      o \(4*a-\frac{5}{2}*a=42\)
      o \(\frac{3}{2}*a=42\)
      o \(a = 28\)
    • On substituting \(a = 28\) in equation (iii), we get
      o Perimeter of rectangle = \(\frac{5}{2}*28=70\) cm…(iv)
    • By equation (i), and (iv), we get
      o Perimeter of triangle =\( 2*70=140\) cm
Hence, the correct answer is Option B.
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Re: The ratio of perimeter of triangle to the perimeter of rectangle be  [#permalink]

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New post 20 Feb 2020, 02:02
Let, the side of square = a cm
So, Length of rectangle = 75a/100 cm = 3a/4 cm
As per question, Ratio of length (L) to breadth (b) of rectangle = 3: 2
Or, L: b = 3:2
Or, 3a/4: b = 3: 2
Or, b = a/2

Perimeter of square = 4a and perimeter of rectangle = 2(a/2 + 3a /4)
= 2(2a/4 + 3a /4)
= 2(5a/4)
= 5a/2
As per question, 4a – 5a/2 = 42
a = 28.
Perimeter of rectangle = 5a/2 = (5*28)/2 = 70 cm
Perimeter of triangle = 2* 70 cm = 140 cm
Answer: B
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Re: The ratio of perimeter of triangle to the perimeter of rectangle be   [#permalink] 20 Feb 2020, 02:02
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