Question Number 181627 by Shrinava last updated on 27/Nov/22
$$\mathrm{Point}\:\:\mathrm{E}\:\:\mathrm{is}\:\mathrm{marked}\:\mathrm{on}\:\mathrm{side}\:\:\mathrm{AD}\:\:\mathrm{in} \\ $$$$\mathrm{rhombus}\:\:\mathrm{ABCD}.\:\mathrm{If}\:\:\mathrm{AC}\:=\:\mathrm{6}\:\sqrt{\mathrm{10}}\:\:\mathrm{and} \\ $$$$\mathrm{BD}\:=\:\mathrm{2}\:\sqrt{\mathrm{10}}\:.\:\mathrm{How}\:\mathrm{many}\:\mathrm{different} \\ $$$$\mathrm{integer}\:\mathrm{values}\:\mathrm{can}\:\mathrm{a}\:\mathrm{piece}\:\mathrm{of}\:\:\mathrm{BE}\:\:\mathrm{take}? \\ $$
Commented by Shrinava last updated on 28/Nov/22
$$\mathrm{Ansser}: \\ $$$$\left.\mathrm{a}\left.\right)\left.\:\left.\mathrm{2}\left.\:\:\:\:\:\mathrm{b}\right)\mathrm{3}\:\:\:\:\:\mathrm{c}\right)\mathrm{4}\:\:\:\:\:\mathrm{d}\right)\mathrm{6}\:\:\:\:\:\mathrm{e}\right)\mathrm{7} \\ $$
Answered by Acem last updated on 28/Nov/22
$$\:{Eight}\:{values}\:;\:{BE}\in\:\mathbb{Z}\:,\:{BE}=\:\left\{\mathrm{11},\:\mathrm{12},\:...,\:\mathrm{18}\right\} \\ $$$$\:{Side}=\:\mathrm{10},\:{Big}\:{diagonal}\:\approx\:\mathrm{18}.\mathrm{97} \\ $$$$ \\ $$