Firstly calculate how many Pythagorean Triples there are that have no component larger than 300.
Next find the sum of all the Hypotenuses from these triples you found in step 1.
Finally add together the results that you received in the first two steps and you'll receive the answer.
By using the method described at this website,
http://www2.math.uic.edu/~fields/puzzle/triples.html
you should be able to convince yourself that there are (1/2)*11*12 = 66 Pythagorean triples for which no side exceeds 300. The largest side will be 11^2 + 12^2 = 265 and there are 11 integer pairs for which that is true, such as (264, 23, 265) and (24, 143, 145).
The sum of the hypotenuses will be
(1^2 + 2^2) + (2^2 + 3^2) + (3^2 + 4^2) + ...((11^2 + 12^2) =
1 + 2(4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100 + 121) + 144 = 1155
The "answer" is 1155 + 66 = 1221
Apparently TchrWill has found some longer Pythagorean combination with side lengths under 300. I agree with his comments and with the website that I referenced, which tells you now to find the allowed combinations.
I have truble mith maths (AND REALLY REALLY VERY NEED HELP!)but at lest i'm REALLY good at english ! (BUT NOT THAT MUCH AT SPELLING!)
The most general formulas for deriving all integer sided rightangled Pythagorean triangles, have been known since the days of Diophantus and the early Greeks. For a right triangle with sides X, Y, and Z, Z being the hypotenuse, the lengths of the three sides of the triangle can be derived as follows: X = k(m^2  n^2), Y = k(2mn), and Z = k(m^2 + n^2) where k = 1 for primitive triangles (X, Y, and Z having no common factor), m and n are arbitrarily selected integers, one odd, one even, usually called generating numbers, with m greater than n. The symbol ^ means "raised to the power of" such that m^2 means m squared, etc.
You can create a table of primitive triple hypotenuses by assuming values of m and n. Such a table would begin with
m............2.....3....4....5....6....7....8....9....10....11....12....13....14....15....16....17
n
1............5....10..17...26..37..50..65..82..101..122..145..170..199..226..257..290
2..................13...............................................................................................293
3........................25.................................................................................265
4..............................41...........................................................................272
5....................................61.....................................................................281
6...........................................85..............................................................292
7...............................................113...............................................274
8.....................................................145.........................................289
9.............................................................181...........................277
10...................................................................221...................296
11...........................................................................265..290
I'll let you fill in the others between these boundries. There are 87 in all..It now must be recognized that these assume k = 1. If you now consider values of k times the hypotenuses derived above, you will have many more.
Note also that the sums of each row values form a finite difference sequence with their third differences being constant. An expression can be derived for the sums of a finite difference sequence but it would probably just as easy to add them up directly.
tyjfgjgf
 👍
 👎
 👁
 ℹ️
 🚩
Answer this Question
Related Questions

Math PLZZ
1. Which set of numbers represents a Pythagorean triple? 6, 9, 12 7, 10, 12 16, 18, 25 27, 36, 45* 2. If the lengths of the legs in a right triangle are 7 and 8, what is the approximate length of the hypotenuse? 1.4 3.8 5.4* 10.6 3. Which set represents a
 asked by YOLO

physics
Calculate the component of a force of 200N at a direction of 60degree to the force.
 asked by Abdulbasit

Pre Algebra Plz help asap!:)
1.Which set represents a Pythagorean triple? 27, 38, 42 33, 44, 55*** 35, 38, 42 68, 72, 81 2.Which number completes the Pythagorean triple: 12, 16, ____? 18 20*** 22 24 3. Which set represents a Pythagorean triple? 1, 2, 4 2, 4, 6 3, 4, 10 5, 12, 13***
 asked by Labbayk

Math
Which of the images above represents a proof of the Pythagorean Theorem? Explain your choice, and then explain how the figure proves the Pythagorean Theorem.
 asked by Eric

Algebra
1. What are the next two terms of the following sequence? 1, 5, 9... A. 27, 211 B. 10,11 C.12,15 D.13,17 2. Which of the following are examples of arithmetic sequences? Choose all that apply. A. 2,2,6,10 B. 1,3,9,27 C. 5,10,20,40 D. 5,1,3,7 3. What is
 asked by Danielle

PHYSICS
Calculate the xcomponent and the ycomponent (in m) of the vector with magnitude 18.0 m and direction 55.0°
 asked by paola

why is physics so hard??????
a velocity vector of 40 degrees below the positive xaxis has a ycomponent of 10 m/s. What is the value of its xcomponent. I know the answer is 11.9 m/s. When I first tried it, I got 6.43 and then I just tried bunch of stuff and I got 11.9 but what I
 asked by apoorva

physics
The drawing shows a force vector vector F that has a magnitude of 600 newtons. It lies at alpha = 67° from the positive z axis, and beta = 31° from the positive x axis. (that's the diagram given) webassign. (delete this space) net/CJ/p139alt.gif (a)
 asked by RE

statistics
set of data is normally distributed with a mean of 200 and standard deviation of 50. · What would be the standard score for a score of 300? · What percentage of scores is between 200 and 300? · What would be the percentile rank for a score of 300?
 asked by Laynette

algebra
The following identity can be used to find Pythagorean triples, where the expressions x2−y2, 2xy, and x2+y2 represent the lengths of three sides of a right triangle; x and y are positive integers; and x>y. (x2−y2)2+(2xy)2=(x2+y2)2 If the sides of a
 asked by jessica

Chemistry
I am doing a lab online and have no clue on how to get started with the following questions? Please Help me! 1. Calculate and record the following (in grams): (a) mass of NaCl by subtraction of other components: (b) measured mass of NaCl after boiling away
 asked by Melissa

College Algebra
What is the Pythagorean Theorem.
 asked by Alicia

physics
a rope attarched to a sledge make an angle of 40 degree with the ground calculate the tension in the rope required to produce a horizontal component of 100N what will be the vertical component of this forces?
 asked by Anonymous

Physics
A block of mass m = 2.00 kg rests on the left edge of a block of mass M = 8.00 kg. The coefficient of kinetic friction between the two blocks is 0.300, and the surface on which the 8.00 kg block rests is frictionless. A constant horizontal force of
 asked by Zac

Math
3. A processor makes two components, A and B, which are then packaged together as the final product (each product sold contains one A and one B). The processor can do only one component at a time: either it can make As or it can make Bs. There is a setup
 asked by Robert

physics
a projectile with a horizontal component of 13m/s and a vertical component of 18 m/s would have an overall velocity of m/s??? at and angle of ?? above the horizontal. Can you please help me fill in the two blanks thank you
 asked by greoge

physics
major leaguer hits a baseball so that it leaves the bat at a speed of 29.0m/s and the angles of 36.9 above horizontal ignore resistance what two time is the baseball at a height of 10.0m above the point at which it left the bat? *what two times is the
 asked by deb

calculus
10. A military jet flies horizontally with a velocity of 450 m/s and 20,000 m above the ground. When the jet is straight above an artillery gun a shell is fired. Assuming the shell hits the jet. a. Calculate the horizontal component of the initial velocity
 asked by Sue

Physical Education
Which of the following is NOT a typical tennis competition? a. Singles b. Doubles c. Triples*** d. Mixed doubles
 asked by Kaai97

Physics
You are traveling in a convertible with the top down. The car is moving at a constant velocity 27.7 m/s, due east along flat ground. You throw a tomato straight upward at a speed of 12.8 m/s. How far has the car moved when you get a chance to catch the
 asked by Chaz
Still need help?
You can ask a new question or browse existing questions.