Menu Close

Category: Mensuration

Let-a-b-and-c-be-three-positive-real-numbers-Prove-that-a-b-c-a-2-bc-b-c-b-2-ca-c-a-c-2-ab-a-b-

Question Number 131465 by bramlexs22 last updated on 05/Feb/21 $${Let}\:{a},{b}\:{and}\:{c}\:{be}\:{three}\:{positive}\:{real}\:{numbers} \\ $$$$.\:{Prove}\:{that}\:{a}+{b}+{c}\:\leqslant\:\frac{{a}^{\mathrm{2}} +{bc}}{{b}+{c}}+\frac{{b}^{\mathrm{2}} +{ca}}{{c}+{a}}+\frac{{c}^{\mathrm{2}} +{ab}}{{a}+{b}} \\ $$ Answered by EDWIN88 last updated on 05/Feb/21 $${According}\:{to}\:{the}\:{identity}\:\frac{{a}^{\mathrm{2}}…

The-perimeter-of-an-isosceles-right-angled-triangle-is-2p-Find-out-the-area-of-the-triangle-

Question Number 99 by sagarwal last updated on 25/Jan/15 $$\mathrm{The}\:\mathrm{perimeter}\:\mathrm{of}\:\mathrm{an}\:\mathrm{isosceles}\:\mathrm{right}−\mathrm{angled} \\ $$$$\mathrm{triangle}\:\mathrm{is}\:\mathrm{2}{p}.\:\mathrm{Find}\:\mathrm{out}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}. \\ $$ Answered by 123456 last updated on 14/Dec/14 $$\mathrm{lets}\:\Delta\mathrm{A}{BC}\:\mathrm{be}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{with}\:\mathrm{lenght}\:{a},{b},{c} \\ $$$$\mathrm{by}\:\mathrm{it}\:\mathrm{isosceles}\:\mathrm{mean}\:\mathrm{that}\:\mathrm{two}\:\mathrm{or}\:\mathrm{more}\:\mathrm{angle}\:\mathrm{and}\:\mathrm{lenght}\:\mathrm{are}\:\mathrm{equal} \\…

What-is-the-area-of-eqilateral-triangle-whose-inscribed-circle-has-a-radius-2-

Question Number 12743 by tawa last updated on 30/Apr/17 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{eqilateral}\:\mathrm{triangle}\:\mathrm{whose}\:\mathrm{inscribed}\:\mathrm{circle}\:\mathrm{has}\:\mathrm{a}\:\mathrm{radius}\:\mathrm{2} \\ $$ Answered by mrW1 last updated on 30/Apr/17 $${OC}=\mathrm{2} \\ $$$${OB}=\mathrm{4}={DO} \\ $$$${CB}=\mathrm{2}\sqrt{\mathrm{3}} \\…

given-T-ABCD-is-pyramid-with-AB-BC-8-and-AT-6-P-is-midpoint-BC-Q-is-midpoint-AT-If-is-the-angle-between-TP-and-PQ-then-cos-is-

Question Number 77272 by jagoll last updated on 05/Jan/20 $$\mathrm{given}\:\mathrm{T}.\mathrm{ABCD}\:\mathrm{is}\:\mathrm{pyramid}\: \\ $$$$\mathrm{with}\:\mathrm{AB}\:=\:\mathrm{BC}\:=\:\mathrm{8}\:\mathrm{and}\:\mathrm{AT}\:=\:\mathrm{6} \\ $$$$\:.\:\mathrm{P}\:\mathrm{is}\:\mathrm{midpoint}\:\mathrm{BC},\:\mathrm{Q}\:\mathrm{is}\:\mathrm{midpoint}\:\mathrm{AT}. \\ $$$$\mathrm{If}\:\alpha\:\mathrm{is}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{between}\:\mathrm{TP}\:\mathrm{and} \\ $$$$\mathrm{PQ}\:\mathrm{then}\:\mathrm{cos}\:\alpha\:\mathrm{is}\:… \\ $$ Commented by john santu last…