Minimum in geometry
Level
pending
ABC is a right isosceles triangle which has AB=AC=10 cm. DEF is also a right isosceles triangle which has DE=DF (D on AB, F on AC, E on BC). Know that the area of DEF is the minimum value. Determine AD.
The answer is 4.000.
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1 solution
Draw EL perpendicular to AB (L on AB). Let EL=a, so LB=a;AD=a. We have: BL+LD+AD=10 2a+LD=10 LD=10-2a Hence AF=10-2a We have: DF^2=AF^2+AD^2=a^2+(10-2a)^2=5a^2+100-40a=5(a-4)^2+20 See that min{DEF}=min(DF^2)/2. Hence min{DEF}=min(5(a-4)^2+20)=> DEF is the minimum value when a=4. So AD=4