A-point-P-is-taken-inside-the-rectangleC-ABD-This-point-joins-the-four-vertices-ofh-te-rectangle-Knowing-that-PA-is-15-cm-B-P-24-cm-and-PC-20-cm-find-the-distancef-o-point-P-from-point-D-

Question Number 200325 by cherokeesay last updated on 17/Nov/23

$$\mathrm{A}\:\mathrm{point}\:\mathrm{P}\:\mathrm{is}\:\mathrm{taken}\:\mathrm{inside}\:\mathrm{the}\:\mathrm{rectangleC} \\ $$$$\mathrm{ABD}.\:\mathrm{This}\:\mathrm{point}\:\mathrm{joins}\:\mathrm{the}\:\mathrm{four}\:\mathrm{vertices}\:\mathrm{ofh} \\ $$$$\mathrm{te}\:\mathrm{rectangle}.\:\:\mathrm{Knowing}\:\mathrm{that}\:\mathrm{PA}\:\mathrm{is}\:\mathrm{15}\:\mathrm{cm}.\:\mathrm{B} \\ $$$$\mathrm{P}\:\:\mathrm{24}\:\mathrm{cm}\:\mathrm{and}\:\mathrm{PC}\:\:\mathrm{20}\:\mathrm{cm}\:\mathrm{find}\:\mathrm{the}\:\mathrm{distancef} \\ $$$$\mathrm{o}\:\mathrm{point}\:\mathrm{P}\:\mathrm{from}\:\mathrm{point}\:\mathrm{D}. \\ $$

Answered by som(math1967) last updated on 17/Nov/23

$${PB}^{\mathrm{2}} +{PC}^{\mathrm{2}} ={PA}^{\mathrm{2}} +{PD}^{\mathrm{2}} \\ $$$$\mathrm{24}^{\mathrm{2}} +\mathrm{20}^{\mathrm{2}} =\mathrm{15}^{\mathrm{2}} +{PD}^{\mathrm{2}} \\ $$$$\Rightarrow{PD}=\sqrt{\mathrm{24}^{\mathrm{2}} +\mathrm{20}^{\mathrm{2}} −\mathrm{15}^{\mathrm{2}} } \\ $$$$=\sqrt{\mathrm{576}+\mathrm{175}} \\ $$$$=\sqrt{\mathrm{751}}=\mathrm{27}.\mathrm{04}{cm}\left({approx}\right) \\ $$

Commented by cherokeesay last updated on 18/Nov/23

$${thank}\:{you}\:! \\ $$

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