Kadille Dave's Pythagoras Growing Post

1) A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c². Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k. A primitive Pythagorean triple is one in which a, b and c are coprime. The name is derived from the Pythagorean theorem, of which every Pythagorean triple is a solution. The converse is not true. For instance, the triangle with sides a = b = 1 and c = √2 is right, but (1, 1, √2) is not a Pythagorean triple because √2 is not an integer. Moreover, 1 and √2 don't have an integer common multiple because √2 is irrational.

If (a, b, c) is a Pythagorean triple,is (ka, kb, kc) for any positive integer k. The name is derived from the Pythagorean theorem, of which every Pythagorean triple is a solution.

a=3x3
b=4x4
c=5x5

a+b=c

9+16=25

2)Find The Missing Side


BubbleShare: Share photos -

3) School Problem Mr. H jumped into a canoe to cross a river. That runs east to west and is 20m wide. The current carried him downstream 8m before he reach the other side. How did he travel in total?

Given: 20m= edge to edge of the river
8m= downstream effect
c= mr. H travelled






This looks how the problem talks about.









solution on how to solve the problem











4) Own Problem

Angelo is planning to slide on a mountain that has a measurement of 156 meters from end to end. There is a building at the summit 10 meters wide and eight meters high. The center of the building is standing exactly on the summit of the building. The summit of the mountain is in the center of the mountain. If someone travel from the summit to the base of the mountain, he will travel 100 metres. The starting point is where the edges of the building is. Find how high did Angelo start sliding?

This diagram shows the labels of sides or measurements in the problem.

The real missing side is from the starting point down to the base of the mountain.
-but the other sides of the triangle are not the exact ones
-there is a building on top of the mountain

letter points
z-distance from the summit to the end of the mountain












Z-the distance from the starting point to the ground that is measured using the slope.











c-distance from the summit to the edge of the mountain.











H - the height of the mountain from the summit down to the base











h- the distance on how high Angelo started sliding from the ground











Q- the distance of the edges of the mountain divided into 2 minus 5









P=Starting Points












plan:
to solve the exact missing sides using: ratio and proportion, subtracting, dividing, and finding the missing side

1. Ratio and Proportion - solve for c
The angle of the small triangle inside the building has the same angle as the whole triangle from one end
















H - the height of the mountain from the summit down to the base
it has a measurement of 62.58 metres













2. Solve for z










3. Solve for Q











Lastly, solve the problem. Because we got the exact measurement of the given sides

a-h(?)
b-q
c-Z

Solution
(click the picture to enlarge)

Kadille's 2nd Growing Post

question no.1

1. in this growing post, i used ratio table because if i got the unit fraction and its value, i can do anything easy and i can explain it clearly, but also the strategies that can be used are money, clock, double, number line and more...

2. i used ratio table or sometimes called T-table or T-chart to show how the fraction change into unit fraction and the value other fraction, ratio tables or T-charts are also used to show patterns.

3. i could use these strategies in solving a problem especially this one and it shows how is the problem solved...

4. in 6 cups... i need to multiply a number into 2 2/5 to get 6.and that number
will be mutiplied into the given information are: 2 2/5 cup container with 1 1/5 cup of spicy shreddies, 4/5 cups of peanuts and 2/5 of pretzels, and the solution will look like this:

5. for 12 cups the ratio table looks like this:

the given infos are given and this will be the ratio table i will use in solving the problem

the first and important thing that i will do to help me to solve the problem in a short period of time, thats why i chose ratio table. i need to find what number will i use to get to 12 cups from 2 2/5 cups. and the solution looks like this: 2 2/5 X n = 12 cups. to find the multiplier (the number that is needed to multiply in multiplicand, and multiplicand is the number to be multiplied to another number which is the multiplier), we need to change the equation to 12 divided by 2 2/5=n but in dividing fractions, all mixed number is needed to be changed to improper fraction and you must get the reciprocal of the equation by inverting the numbers and changing the division symbol to multiplication symbol and the solution looks like: 12 x 5/12=n that makes it easy to solve so the answer and our multiplier will be 5. and the number five will be multiplied to the given number of cups with all ingredients, price, cups of spicy shreddies, cup of peanuts, and cups of pretzels to get the exact value of each ingredient to the exact cups and price.
the solution look like this:



i hope you can see how i used the ratio table and how i used number five as my multiplier, now the answer is now being shown and it serves as my conclusion for finding the price and the cups of the ingredients of 12 cups


*i used multiplication because the one that needs to solve is higher than the given number, reverse in division.



in 1/2 we will do the same process as the other one but 1/2 cup is lower than the given number of cups so the solution will be in reverse.* now i will show you the ratio tale with the given infos for 1/2:
















in the solution that i did for 12 cups i did it here in reverse, i will get the divisor, like the multiplier of 12 which is 5, and i will divide it into the given informations
so the solution to get the divisor is 2 2/5 / n = 1/2. i will make the equation to the better one and it looks like this: 2 2/5 / 1/2 = n. now the answer of that equation would be 4 4/5, but in dividing fractions, the mixed numbers must be changed into improper fractions and because it is a divisor we will get its reciprocal by inverting the numbers in the fractions so the improper fraction of 4 4/5 id=s 24/5. now that i got my divisor i will show you how it is being solved:



now you can see how i solve the two fractions in reverse, i hope you will understand what is the real use of ratio table and the reason why i chose ratio table...i love ratio table... i really love it! it is perfect to use ratio table in this problem, i just learned ratio table this year and i love the use of this strategy or method for solving a problem like this.






in 1 cup, the procedure in solving this problem is the same as 1/2 cup...now the easy thing is i had the records of 1/2, i will just multiply it to 2 to get one cup and the results is shown like this:

for question number 2



for question number three:



for the fourth question in this growing post