Question #5150

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

Expert's answer

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

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

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