I think it is time for us to have a new puzzle thread

THIS THREAD WILL BE AVAILABLE IN THE STICKY TOPICS

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There are lots of good puzzles in this maths is fun site.

"Samuel Loyd (January 31, 1841 - April 10, 1911), perhaps Americas greatest ever puzzle maker, invented and refined thousands of puzzles in his lifetime. Word puzzles, rebuses, tangrams and math puzzles. Here we have collected some of his best math puzzles from his Cyclopedia of Puzzles for your enjoyment." (Mathsisfun)

https://www.mathsisfun.com/puzzles/sam-loyd-puzzles-index.html

CPhill introduced me to Sam Loyd puzzles here: Thanks Chris

https://web2.0calc.com/questions/how-much-do-they-weigh

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Here is an old puzzled threads (December 2015)

Melody
Sep 24, 2017

#1**+2 **

Here's one to begin the thread!

The leg of a right triangle is \(\frac{1}{3}\) the sum of the other sides, and the perimeter is 12 units. What is the area of this traingle?

Good luck to any participants!

TheXSquaredFactor
Sep 24, 2017

#3**+1 **

Thanks XSquared

Chris has already answered and that is great but I have a suggestion.

**How about people answer on a new question thread and then put in an answer link.**

That way the answer is not right with the question. It is more like having to look up the back of the book for the answer.

This might not work for a lot of people and that is fine, it is just a suggestion

Melody
Sep 24, 2017

#2**+3 **

The leg of a right triangle is 1/3 the sum of the other sides, and the perimeter is 12 units. What is the area of this traingle?

Let a, b be the legs and c the hypotenuse

So

a^2 + b^2 = c^2 ⇒ a^2 = c^2 - b^2 ⇒ a = sqrt ( c^2 - b^2 )

3a = b + c

a + [b + c] = 12

a + 3a = 12

4a = 12

a = 3

This implies that c^2 - b^2 = 9

And b + c = 9

So

c^2 - b^2 = b + c

(c - b) (c + b) = (b + c) divide through by (b + c)

So

(c - b) = 1 ⇒ c = b + 1

So

b + ( b + 1) = 9

2b = 8

b = 4 and c = 5

And the area is just the product of the legs / 2 = a * b / 2 = 3 * 4 / 2 = 6 units^2

CPhill
Sep 24, 2017