If ED = 23 , and the value of the side of the square ABCD is a multiple of 11, what is the area of the red triangle AFE?! Find the very shortest way to solve this puzzle and use only basic geometry, trigonometry is not allowed.
What is the area of triangle AFE?
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geometry
puzzle
triangles
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0@user3196,I see now,you are right – 2011-09-17
2 Answers
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Let $AB = 11x$. Triangles EDF and EAB are similar, so:
$\dfrac{ED}{EA} = \dfrac{DF}{AB}$
$\dfrac{23}{23 + 11x} = \dfrac{DF}{11x}$
$DF = \dfrac{253x}{23 + 11x}$
The area of $\triangle AFE$ is thus
$\dfrac{1}{2} \cdot EA \cdot DF = \dfrac{1}{2} \cdot (23 + 11x) \cdot \dfrac{253x}{23 + 11x} = \dfrac{253}{2}x$
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0you can't calculate exact value of triangle if you dont have any more conditions,for example instead of x you can take 33,44,55, and so on. 11*x in general for x>2 – 2011-09-17
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let us consider one simple situation,suppose AB=33; you can check that 33 is multiple of 11,33/11=3,and also we know that DF/FC=1/2
.if we denote DF by x,then FC=2*x
so x+2*x=33, 3*x=33 x=11;(sorry in first coment instead of DC should be FC) so DF=11;
length of AE=AD+DE or 33+23=56,so are of AEF=1/2*DF*AE`=1/2*56*11=28*11=308