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Question Number 204236 by Panav last updated on 09/Feb/24

Helpful questionfor Olympiads, Find Sol^n .

$$\boldsymbol{{Helpful}}\:\boldsymbol{{questionfor}}\:\boldsymbol{{Olympiads}},\:\boldsymbol{{Find}}\:\boldsymbol{{Sol}}^{\boldsymbol{{n}}} . \\ $$

Commented by Panav last updated on 09/Feb/24

Answered by JDamian last updated on 10/Feb/24

R=14 cm  2×S_(triangle) = R^2 cos^2  45° = (R^2 /2) = 98   cm^2   S_(full circle) =  πR^2   =  196π    cm^2     S = 196π−98   cm^2   196π−98   ∉ N

$${R}=\mathrm{14}\:\mathrm{cm} \\ $$$$\mathrm{2}×{S}_{{triangle}} =\:{R}^{\mathrm{2}} \mathrm{cos}^{\mathrm{2}} \:\mathrm{45}°\:=\:\frac{{R}^{\mathrm{2}} }{\mathrm{2}}\:=\:\mathrm{98}\:\:\:\mathrm{cm}^{\mathrm{2}} \\ $$$${S}_{{full}\:{circle}} =\:\:\pi{R}^{\mathrm{2}} \:\:=\:\:\mathrm{196}\pi\:\:\:\:\mathrm{cm}^{\mathrm{2}} \\ $$$$ \\ $$$${S}\:=\:\mathrm{196}\pi−\mathrm{98}\:\:\:\mathrm{cm}^{\mathrm{2}} \\ $$$$\mathrm{196}\pi−\mathrm{98}\:\:\:\notin\:\mathbb{N} \\ $$

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