Question

Area of a rectangle with integer values for its sides, is 8 times its perimeter.
What are its sides ?

Answer 1

let's denote it's sides as a,b
then area is ab, perimeter is 2(a+b)
ab=8*2(a+b)
ab=16a+16b
a=16 a/b+16
we can take a/b=1 hence a=32=b
then ab=32*32=16*(32+32)=16*2*32=32*32 right
so possible answer is 32,32
also we can take a/b=2 hence a=48, b=24
a/b=4 is also possible => a=80, b=20