Uneven sides

Geometry Level 3

Bob has a paper that its width is 30cm, By using special scissors he cuts the paper into two pieces, such that triangular shape is formed.

given that $AB = BC = 1$ cm and the angle $\angle{ABC} = 120$ degrees

Calculate for him what will be the total length of the triangular edge(AB+BC+...untill the end)

15\sqrt{3}

10

60

20\sqrt{3}

20

1 solution

Nibedan Mukherjee
Jan 16, 2019

Nice solution, Adding to the above, It will be really nice to keep in mind that the ratio between the width and AC is how many triangles fit inside this paper. For every triangle, we cover AB+BC distance. So, Number of triangles times Distance per unit triangle is the total distance.

Bar Kam - 2 years, 4 months ago

spot on! the real problem was with my math editor soft.... had to use MS paint as an auxiliary..

nibedan mukherjee - 2 years, 4 months ago

But how can the zig-zag line be shorter than a straight line??

And why did you say $10\sqrt 3 \times \sqrt 3 = AB+BC+\cdots+KL$ , shouldn't it be $10\sqrt 3 \times 2$ ?

Henry U - 2 years, 4 months ago

Thanks for mentioning it!

nibedan mukherjee - 2 years, 4 months ago

@Brilliant Mathematics could you change the answer to $\boxed{20\sqrt 3}$ ? Thanks!

Henry U - 2 years, 4 months ago

Yep, you are correct I didn't notice

Bar Kam - 2 years, 4 months ago

Thanks. I've updated the options and answer to reflect this.

Brilliant Mathematics Staff - 2 years, 4 months ago

Uneven sides

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