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Explain The Pythagorean Relationship
1) Can be used to determine the lenth of a hypotenuse of the right triangle when two lents of the two legs are known.
2) The sum of the areas of squares attached to the legs of a right triangle equals the area of the square attached to the hypotenuse.
3) It's also the relationship between the lenths of a right triangle.
1.The Pythagorean relation ship is the relation ship between the sides of the triangle
2. a + b = c the side length of the triangle 12+5= c (12x12)+(5x5)=c 144 + 25=c 169 =C 13=c
3.a + b = c no the triangle isn't a right one. 8 + 6 = 11 (8x8)+(6x6)=(11x11) 64 + 36 = 121 100 = 121 nope
Q#1 what are the areas of the three squares.-92-(4) a-30x30=9004 b-40x40=1600 c-50x50=2500
Q#2 carmel want to mount a 18cmx18cm picture on a square board that is 4 times the area of the picture. a-324 b-1296 c-?
Q#3 the hypotenuse of the triangle cuts the circle in half. what is the diameter of the circle. Express your answer to the nearest tenth of a centimeter. a + b =c 7 +5 =c 7x7+ 5x5 =c 49 + 25 = c 74 =c 8.6 =c
I know that to make 144, you can square the number 7 by itself to get your answer.
The square of a whole number is a perfect square because if you used 1 block for every unit in the square and had groups of 7 by 7, the length and the area of the square would be the same.
I found the Prime Factors of 12 which is 6 and 2. (6 x 2 = 12)
Then I found the Prime Factors go 6 and got 3 and 2. (3 x 2)
I boxed in the Line of Prime Factorization and then made a basket using those numbers just to get a clearer understanding.
This resulted into a perfect square.
B.)
Since there is no number that can be multiplied by itself to get 60, I divided 60 to get 30.
The Prime Factors of 60 would be 30 and 2.
I knew that 3 x 10 would equal 30, and that would be a Prime Factor for that.
Finally, I took the number 10 and divided it again to get 5 x 2.
The Line of Factorization did not all have even sets of numbers if you would put it in a basket, therefore it is not a perfect square.
D.)
Again, I know that there is no square number to make 40, so I just used the prime numbers 5 and 6. (5 x 6= 40)
Then I knew that 3 x 2 would make 6.
The Line of Factorization would be 5 x 3 x 2, which means you can't basket the numbers evenly.
40 is not a perfect square.
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Solution:
For 15 a), since I knew that 7 x 7 would equal 49, I used that as my Prime Factor.
Notice that 7 x 7 makes a Perfect Square.
In the second example I showed how I got the area, which is just side x side.
When you prime factor a square you can find either side lengths or square roots.
the square root of 49 = 7, which also equals to the square root of 7 squared, which is also 7.
For a), what I did was multiply the numbers on the side (9 x 4 = 36) because I know that sxs= area. The answer would be 36m2.
For b), I first used my calculator to find out what the square root of 36 was. I got the answer 6, so for that, I know that 6 x 6 makes a perfect square and equals to 36.
The boxed numbers are the Line of Prime Factorization.
I also used a basket after to help make it more understandable.
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Here is a helpful video for a better understanding:
*Sorry if the video is confusing at the end!
Here is a game you might want to play in Mangahigh that is really fun ;)
THANKS FOR GIVING YOUR TIME AND EFFORT INTO READING THIS! Help me out if I have made any mistakes :)
1. Pythagorean relationship is when one number gets doubled and added to get a total value on a triangle. 2. Pythagorean relationships means a total value. 3. an example of Pythagorean is 2+4=6 4. the Pythagorean means a value of an triangle
4) Estimate the square root of each number, to one decimal. Check with a calculator.
a) 72 b) 103 c) 55
10. Kai uses an entire can of paint on a square backdrop for the school play. The label on the can states that one can cover 27 m² of wall surface. Estimate the backdrop's side length, to one decimal place.
.
5x5=25 and 6x6=36 so it should be between the numbers 5 and 6.
5.2x5.2=27.04 then it move it up into one decimal place which is 5.3
15. Order the following numbers from least to greatest: 7, square root of 46, 5.8, square root of 27, and 6.3.
5.1, 5.8, 6.3, 6.7, 7
1) Answer in a short paragraph with diagrams
2. Solve for the missing side length.
3. Is this a right triangle? Prove it!!!
This is not a right triangle because 100 cm does not equal 121 cm
This link will help you understand Pythagorean Relationship even more
Is This A Right Triangle? Prove It!
