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ABCD-is-a-rectangle-such-that-AB-gt-BC-and-O-is-the-mid-point-of-DC-if-OB-0-1m-and-BOC-find-an-expression-for-the-perimeter-of-the-rectangle-in-terms-of-Find-also-the-values-of-




Question Number 188260 by Humble last updated on 28/Feb/23
ABCD is a rectangle such that   ∣AB∣>∣BC∣ and O is the mid−point   of DC, if ∣OB∣=0.1m and ∠BOC =𝛉,   find an expression for the perimeter of   the rectangle in terms of 𝛉. Find also,   the values of R and 𝛃 for which the   perimeter is Rcos(𝛉−𝛃). Deduce, the   greatest possible value oc the perimeter.
$$\boldsymbol{{ABCD}}\:{is}\:{a}\:{rectangle}\:{such}\:{that} \\ $$$$\:\mid\boldsymbol{{AB}}\mid>\mid\boldsymbol{{BC}}\mid\:{and}\:{O}\:{is}\:{the}\:{mid}−{point} \\ $$$$\:{of}\:\boldsymbol{{DC}},\:{if}\:\mid\boldsymbol{{OB}}\mid=\mathrm{0}.\mathrm{1}{m}\:{and}\:\angle\boldsymbol{{BOC}}\:=\boldsymbol{\theta}, \\ $$$$\:{find}\:{an}\:{expression}\:{for}\:{the}\:{perimeter}\:{of} \\ $$$$\:{the}\:{rectangle}\:{in}\:{terms}\:{of}\:\boldsymbol{\theta}.\:{Find}\:{also},\: \\ $$$${the}\:{values}\:{of}\:\boldsymbol{{R}}\:{and}\:\boldsymbol{\beta}\:{for}\:{which}\:{the}\: \\ $$$${perimeter}\:{is}\:\boldsymbol{{Rcos}}\left(\boldsymbol{\theta}−\boldsymbol{\beta}\right).\:{Deduce},\:{the}\: \\ $$$${greatest}\:{possible}\:{value}\:{oc}\:{the}\:{perimeter}. \\ $$

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