Question

Geometry Question

Answer 1

What is it?

Answer 2

\(\text{ABC is an equilateral triangle. Point D is on AC and Point E is on BC, }\\
\text{such that AD=2CD and CE=EB. If we draw perpendiculars from D and E }\\
\text{to other two sides and find the sum of the length of two perpendiculars }\\
\text{for each set, that is, for D and E individually }\\
\text{and denote them as per (D) and per(E), then which}\\
\text{ of the following option will be correct. }\)

\(\text{1) per (D) > per (E)}\\
\text{2) per (D) = per (E)}\\
\text{3) per (D) < per (E)}\\
\text{4) None of these}\\\)

Answer 3

\(DF = DC\sin 60\)
\(DG=AD\sin 60\)

\(DF+DG=(DC+AD)\sin 60 = AC\sin 60\)

Answer 4

by similar reasoning the sum of perpendiculars from \(E\) equals \(BC\sin 60\)

Answer 5

since \(AC=BC\), the sums of perpendiculars are equal

Answer 6

COOL