Please only solve 7, 8 and 9, showing your work as you go. Thank you so much! Ar

Question

Please only solve 7, 8 and 9, showing your work as you go. Thank you so much!

Archimedes, approximation to 427 3. First note that triangle ABD and triangle BEF are similar. Also note that BE =s/2-s812. Use these facts to show that = s 4. Next note that triangle ACF and triangle CFG are similar. Use this fact to show that s,12 1 8-4 or 2 Having related the side lengths of the various polygons, we now relate the perimeters of the polygons. We let S4 = 484 be the perimeter of the circumscribed square, T4 44 be the perimeter of the inscribed square Sg 8sg be the perimeter of the circumscribed octagon, and Ts-81g be the perimeter of the inscribed octagon. Use these definitions in Steps 3 and 4 to show that 5. 4 +T an

Explanation / Answer

ans 7.

n Sn Tn (Sn+Tn)/2 4 4 2.828427 3.414214 8 3.313708 3.061467 3.187588 16 3.182598 3.121445 3.152022 32 3.151725 3.136548 3.144137 64 3.144118 3.140331 3.142225 128 3.142224 3.141277 3.14175 256 3.14175 3.141514 3.141632

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