Hello fellow humans. My confusion is on the dimensions of objects. I noticed that if 3 shapes are made, **A**, **B** and **C**, all quadrilaterals. **A** is a **5x5**, **B** is a **6x4** and **C** is a **8x2**. The perimeter of all shapes are the same, 20, but their areas differ. Please indulge my inquisitiveness.

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TopNewestWell it means that 2(l+b)=20 l+b=10. But this does not mean, that the area , lb, is fixed. l=8, b=2, gives lb=16. l=5,b=5 gives lb=25. l=6,b=4 gives lb=24. – Shourya Pandey · 4 years, 5 months ago

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– Ibukunoluwa Abiodun · 4 years, 5 months ago

But why are their areas different in such a way that the area tends to be more towards the square shapes :)Log in to reply

– Shourya Pandey · 4 years, 5 months ago

That is because: Suppose l>=b, without loss of generality. Say l=5+d. then b=5-d So lb=(5+d)(5-d)=25-d^2. So as l and b come closer to resemble a square, i.e., l=b=5, then d becomes smaller and smaller and the area increases.Log in to reply

– Shourya Pandey · 4 years, 5 months ago

Another way is the A.M.-G.M. inequality, stating \(\frac {l+b}{2}\)>= \(\sqrt lb\) So that lb<=25, with equalty iff l=b=5, i.e., the figure is a square.Log in to reply

– Ibukunoluwa Abiodun · 4 years, 5 months ago

Thanks a lot, now I have full light to my darkness, thanks to you. Man you are good :)Log in to reply