Geometry Problems, Math Problems

Problem of the Day: 2/8/13

In the figure below, the side length of the octagon is 4 cm. What is the length of the diagonal shown? Express your answer in simplest radical form.

20130208-065814.jpg

Solution to yesterday’s problem:

We can imagine a diagonal going across the square which also serves as a diameter of the circle. The diagonal would split the square into two right triangles, and we could find the length of the diagonal using the Pythagorean Theorem.

(6)^2+(6)^2=x^2

36+36=x^2

72=x^2

x=6\sqrt{2} (after simplification)

You may recognize this as a 45-45-90 triangle, in which case you didn’t have to do all that work. Anyway, if the diagonal/diameter is 6\sqrt{2} inches, then the radius will be half that, or 3\sqrt{2} inches.

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