Find the altitude

Geometry Level 3

Equilateral triangle C E F CEF is inscribed in rectangle A B C D ABCD . Altitude B G = 7 BG=7 and altitude A H = 22 AH=22 , find the length of altitude D M DM .


The answer is 15.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

a r e a △ A E F = a r e a △ E B G + a r e a △ C D F area~\triangle AEF=~area~\triangle EBG+~area~\triangle CDF

( E F ) ( A H ) 2 = ( E C ) ( B G ) 2 + ( C F ) ( M D ) 2 \dfrac{(EF)(AH)}{2}=\dfrac{(EC)(BG)}{2}+\dfrac{(CF)(MD)}{2}

since E F = E C = C F EF=EC=CF , we have

22 = 7 + M D 22=7+MD

M D = 15 \color{#D61F06}\boxed{MD=15}

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And how do you know the area of triangle A E F AEF is the sum of the areas of triangles E B C EBC and C D F CDF ?

Jon Haussmann - 3 years, 7 months ago

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I have the same question. Really an elegant result!

Ujjwal Rane - 3 years, 6 months ago

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