A triangular geometry problem 1

Geometry Level 3

As shown in the image, CAB is an isosceles right triangle with perpendicular length 1. A line parallel to CB is drawn through point A and labeled DE. Then, from point C, a line CG is drawn and is equal to CB. Find the length of the perpendicular line from point G to line AB, and leave your answer to 3 decimal places.


The answer is 0.366.

A I by A I , 17, United Kingdom

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1 solution

Marta Reece
Apr 6, 2018

In triangle DGC we have D G = ( 2 ) 2 − 1 ( 2 ) 2 = 3 2 DG=\sqrt{(\sqrt2)^2-\frac1{(\sqrt2)^2}}=\frac{\sqrt3}{\sqrt2}

A G = D G − D A = 3 2 − 1 2 AG=DG-DA=\frac{\sqrt3}{\sqrt2}-\frac1{\sqrt2}

Answer = A G 2 = 3 − 1 2 ≈ 0.366 =\frac{AG}{\sqrt2}=\frac{\sqrt3-1}2\approx\boxed{0.366}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Thanks for adding a solution! I actually approached this problem in a very different way, which is forming an equation for x ( the perpendicular line) using the right triangle with the hypotenuse GB, and it is very interesting to see different solutions!

A I - 3 years, 2 months ago

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