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Geometry Level 1

The polygonal path connecting points A and B forms 7 equilateral triangles.

If the distance between point A to point B is 20 units, then how long is the distance of the path (in units)?

The answer is 40.

4 solutions

José Mendes
Feb 29, 2016

Since all triangles are equilateral and have their base on the segment AB, and the AB segment is the totally composed by the 7 triangles' base, everytime we move a distance of $x$ on the AB segment, on the path we will need to walk the two other sides of the triangle, ie $2x$ .

Therefore, if $x=20$ , the path will be $2x=40$

same way like mendes

Arun Garg - 5 years, 2 months ago

One can easily rearrange the segments of the path so they form two sides of a single equilateral triangle with a base length 20. So the length of the path is the lengths of these two sides = 2 x 20 = 40.

Lishan Aklog - 1 year, 6 months ago

nice solution, upvoted!

Natanael Flores - 5 years, 3 months ago

Roy Bertoldo
Dec 4, 2016

Denote the 7 segments of the line AB as x₁, x₂, x₃, x₄, x₅, x₆, x₇, and the length of the broken line as L,

Since the sum of two sides of an equilateral triangle = 2 times the third side

L = 2x₁+2x₂+2x₃+2x₄+2x₅+2x₆+2x₇

L = 2(x₁+x₂+x₃+x₄+x₅+x₆+x₇) = 2(20) = 40

Shashwat Gupta
Mar 1, 2016

All the triangles are equilateral so sum of their base would be 20 Therefore sum of their 2 sides would be 40

Arya Saranathan
Aug 20, 2019

Since we know the number or positioning of the triangles will not affect the solution, we can greatly simplify the problem by assuming the 'path' is made up of just one, big equilateral triangle.

From there, the 'path' is just two sides of that triangle, yielding

$2*20=40$

Cardiac Monitoring

The answer is 40.

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