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Question

In an equilateral triangle ABC, AD is drawn perpendicular to BC meeting BC in A. If (AD)2=x(BD)2. Find x.

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Solution

Equilateraltriangle,
A=B=C=60
InABD:
tan(B)=ADBD
tan(60)=ADBD
3=ADBD
squaring
AD2=3BD2
x=3

1007671_1055325_ans_1e9a2e41254d4e3fb0d0ad51fb845185.png

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