Raising the flag

Geometry Level 3

Figure above shows two right triangles $DAB$ and $ABC$ with right angles at $A$ and $B$ respectively. With $E$ is the point of intersection between the straight lines $BD$ and $AC$ . If we drop a straight line from $E$ that is perpendicular to the base $AB$ and intersect at $AB$ at point $F$ , find the distance $EF$ in $\text{cm}$ .

The answer is 4.8.

2 solutions

Mark Yates
Jul 22, 2015

FB/EF=(AF+FB)/12 and AF/EF=(AF+FB)/8 by similar triangles solve both for AF+FB then set them equal 12FB/EF=8AF/EF therefore AF=3FB/2 eliminate AF using the above relation so, (3FB/2)/EF=(5FB/2)/8 eliminate FB's and get EF=24/5 It is interesting to note that as the poles are moved farther and farther apart EF does not change height.

Marta Reece
Mar 10, 2017

Triangles $CEB$ and $AED$ are similar with a ration of sides $2:3$ .

Specifically the lengths of the sides $CE$ and $EA$ are $2:3$ .

Their projections onto $BC$ , which are $GC$ and $GB$ , will also be $2:3$ .

So $GB=BC\times\frac{3}{2+3}=8\times\frac{3}{5}=\frac{24}{5}=4.8$ .

But $GB=EF$ .

Raising the flag

The answer is 4.8.

2 solutions

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