Caroline
Apr 27th, 2007
Apr 27th, 2007
Math Brain Teaser: The Unkindest Cut of All, Part 1 of 2
In honor of Mathematics Awareness Month 2007: Mathematics and the Brain, here is another mathematical brain bender from puzzle master Wes Carroll ...
The Unkindest Cut of All, Part 1 of 2
Difficulty: HARD
Type: MATH (Spatial)
Question:
The area of a square is equal to the square of the length of one side. So, for example, a square with side length 3 has area (32), or 9. What is the area of a square whose diagonal is length 5?
In this puzzle you are working out your spatial visualization (occipital lobes), memory (temporal lobes), and hypothesis generation (frontal lobes).
Click to read the Solution and Explanation.
Go on to Concentric Shapes: The Unkindest Cut of All, Part 2 of 2
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I feel the solution is too long, easiest thing to do is:
you know that the diagonal is sq.rt(2)*x where x is the measurement of the side. since that's true, then swuare the answer nd you're done. so [5/2qrt(2)]^2 = 12.5
There is another easy way:
The diagonal divides the square in two triangles. Each triangle has an area of bxh/2
b = diagonal
h = diagonal / 2
so 5 x 2.5 / 2 = 6.25
6.25 x 2 triangles = 12.5
I think you would have to set the difficulty to Easy.
Bye.
I concur!
12.5
a^2 + b^2 = c^2
You square the length of the diagonal (C).
25 = a^2 + b^2
because its a square both sides are equal. So divide by 2 to get the square of 1 of the sides ie the volume.
Notice two diagonal lines, one for each pair of opposing corners of the square, form four halves of 2 squares. The length of the side of any of these halves is equal to half of 5, or 2.5. The area of a square is one of its sides squared, 2.5^2 = 6.25 * 2 = 12.5, as (again) there are four halves of two squares.