a square and a reactangle have the same perimeter of 80 cm. if the difference between their areas is 100 cm find the sides of the rectangle.
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perimeter of square =4×s ;
perimeter of rectangle =2(l+b),
area of square =s×s,
area of rectangle =l×b ,
4×s=2(l+b)=80,
4×s =80,
s=20cm ,
2(l+b)=8 =l+b=40cm ,
l=40-b,
.: A/Q ,
s×s - l×b= 100,
s×s - (40-b)=100,
20×20-40b+b^2=100
on solving ,
b=10 or 30,
putting the value , in 80=2(l+b),
l=10 ,
.: b= 30 and l=10
perimeter of rectangle =2(l+b),
area of square =s×s,
area of rectangle =l×b ,
4×s=2(l+b)=80,
4×s =80,
s=20cm ,
2(l+b)=8 =l+b=40cm ,
l=40-b,
.: A/Q ,
s×s - l×b= 100,
s×s - (40-b)=100,
20×20-40b+b^2=100
on solving ,
b=10 or 30,
putting the value , in 80=2(l+b),
l=10 ,
.: b= 30 and l=10
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