Origami Logic Part 1

Geometry Level 2

Stated in the picture is how to divide a paper into equal pieces. What is the ratio of the length BE to length EC? Key in your answers in the form:

$\frac { Length\quad BC }{ Length\quad EC } =\quad answer\quad (rounded\quad off\quad to\quad the\quad nearest\quad whole\quad number)$

The answer is 3.

1 solution

Julian Poon
May 17, 2014

Consider this image: https://docs.google.com/document/d/1CVOOfHrMjD81taOO6fp_f-Y3AdEeIZfCzv4cEVtYEuw/edit

$We\quad can\quad find\quad { θ }_{ 1 }\quad and\quad { θ }_{ 2 }\\ \\ tanθ_{ 1 }=\frac { x }{ 2x } =0.5\\ θ_{ 1 }=tan^{ -1 }0.5\\ θ_{ 2 }=180-45-θ_{ 1 }=135-{ tan }^{ -1 }0.5\\ Using\quad the\quad Sine\quad Rule,\quad we\quad can\quad find\quad y_{ 2 }\\ \\ Sine\quad rule:\\ \\ \frac { 2x }{ sinθ_{ 2 } } =\frac { y }{ sinθ_{ 1 } } \\ y=\frac { 2xsinθ_{ 1 } }{ sinθ_{ 2 } } \\ \\ We\quad can\quad find\quad y_{ 2 }\quad too,\quad using\quad Pythagoras\quad theorem.\\ \\ y_{ 1 }=\sqrt { 8{ x }^{ 2 } } \\ \\ So,\quad if\quad you\quad try:\\ \\ \frac { y_{ 1 } }{ y_{ 2 } } =\quad 3$

Origami Logic Part 1

The answer is 3.

1 solution

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