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

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