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Question Number 9589 by tawakalitu last updated on 19/Dec/16

Answered by ridwan balatif last updated on 19/Dec/16

Commented by tawakalitu last updated on 19/Dec/16

i really appreciate sir. God bless you.

$$\mathrm{i}\:\mathrm{really}\:\mathrm{appreciate}\:\mathrm{sir}.\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}. \\ $$

Answered by mrW last updated on 19/Dec/16

a+b=AB=10 ...(i) b+c=BC=11 ...(ii) c+a=AC=9 ...(iii) (ii)+(iii)−(i): 2c=9+11−10=10 c=5=CD ⇒answer (C)

$$\mathrm{a}+\mathrm{b}=\mathrm{AB}=\mathrm{10}\:\:\:...\left(\mathrm{i}\right) \\ $$$$\mathrm{b}+\mathrm{c}=\mathrm{BC}=\mathrm{11}\:\:\:...\left(\mathrm{ii}\right) \\ $$$$\mathrm{c}+\mathrm{a}=\mathrm{AC}=\mathrm{9}\:\:\:...\left(\mathrm{iii}\right) \\ $$$$\left(\mathrm{ii}\right)+\left(\mathrm{iii}\right)−\left(\mathrm{i}\right): \\ $$$$\mathrm{2c}=\mathrm{9}+\mathrm{11}−\mathrm{10}=\mathrm{10} \\ $$$$\mathrm{c}=\mathrm{5}=\mathrm{CD} \\ $$$$\Rightarrow\mathrm{answer}\:\left(\mathrm{C}\right) \\ $$

Commented by tawakalitu last updated on 19/Dec/16

i really appreciate sir. God bless you.

$$\mathrm{i}\:\mathrm{really}\:\mathrm{appreciate}\:\mathrm{sir}.\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}. \\ $$

Commented by mrW last updated on 20/Dec/16

Commented by tawakalitu last updated on 20/Dec/16

I really appreciate. God bless you sir.

$$\mathrm{I}\:\mathrm{really}\:\mathrm{appreciate}.\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$

Answered by richard last updated on 21/Dec/16

Hey there! It is my first post here! I hope i can be useful even still being a high school student kk So, for me, this question doesn′t even need to calculate anything, because it can be answered by a logical thought: Right, if you pain atention, you will see that in the triangle ΔABC, with the sides AB=10, that just by looking at the image, the sides CD are equal to half the value of AB. Then:((CD≡((AB)/2)) , or yet (AB≡ 2CD)) So, if that thought is correct, it means CD= 5 ⇒answer: letter (C)

$$\mathrm{Hey}\:\mathrm{there}!\:\mathrm{It}\:\mathrm{is}\:\mathrm{my}\:\mathrm{first}\:\mathrm{post}\:\mathrm{here}!\:\mathrm{I}\:\mathrm{hope}\:\mathrm{i}\:\mathrm{can}\:\mathrm{be}\:\mathrm{useful}\:\mathrm{even}\:\mathrm{still}\:\mathrm{being}\:\mathrm{a}\:\mathrm{high}\:\mathrm{school}\:\mathrm{student}\:\:\mathrm{kk} \\ $$$$\mathrm{So},\:\mathrm{for}\:\mathrm{me},\:\mathrm{this}\:\mathrm{question}\:\mathrm{doesn}'\mathrm{t}\:\mathrm{even}\:\mathrm{need}\:\mathrm{to}\:\mathrm{calculate}\:\mathrm{anything},\:\mathrm{because}\:\mathrm{it}\:\mathrm{can}\:\mathrm{be}\:\mathrm{answered}\:\mathrm{by}\:\mathrm{a}\:\mathrm{logical}\:\mathrm{thought}: \\ $$$$\mathrm{Right},\:\mathrm{if}\:\mathrm{you}\:\mathrm{pain}\:\mathrm{atention},\:\mathrm{you}\:\mathrm{will}\:\mathrm{see}\:\mathrm{that}\:\mathrm{in}\:\mathrm{the}\:\mathrm{triangle}\:\Delta\mathrm{ABC},\:\mathrm{with}\:\mathrm{the}\:\mathrm{sides}\:\mathrm{AB}=\mathrm{10},\:\mathrm{that}\:\mathrm{just}\:\mathrm{by}\:\mathrm{looking}\:\mathrm{at}\:\mathrm{the}\:\mathrm{image},\:\mathrm{the}\:\mathrm{sides}\:\mathrm{CD}\:\mathrm{are}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{half}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{AB}.\:\mathrm{Then}:\left(\left(\mathrm{CD}\equiv\frac{\mathrm{AB}}{\mathrm{2}}\right)\:,\:\mathrm{or}\:\mathrm{yet}\:\left(\mathrm{AB}\equiv\:\mathrm{2CD}\right)\right) \\ $$$$\mathrm{So},\:\mathrm{if}\:\mathrm{that}\:\mathrm{thought}\:\mathrm{is}\:\mathrm{correct},\:\mathrm{it}\:\mathrm{means}\:\mathrm{CD}=\:\mathrm{5} \\ $$$$\Rightarrow\mathrm{answer}:\:\mathrm{letter}\:\left(\mathrm{C}\right) \\ $$

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