PYTHAGOREAN TRIPLE GENERATOR
About "Pythagorean triple generator"
"Pythagorean triple generator" is the stuff related to forming a right triangle for which the lengths of the three sides are created.
For example, a teacher wants to give a question to the students related to right triangle.
She wants to create a question like "Find the missing side of the right triangle".
But she does not know, how to fix the lengths of the other two sides which can meet the condition of right triangle.
Here is the idea.
We can use the following formulas to form a right triangle.
Hypotenuse = m² + n²
Leg = m² - n²
Leg = 2mn
And always m > n
In the above formulas, you can take any positive values for "m" and "n" to get the three sides of a right triangle with the condition m > n.
For example, let m = 3, n = 2
Then,
hypotenuse = m² + n² = 3² + 2² = 9 + 4 = 13
leg = m² - n² = 3² - 2² = 9 - 4 = 5
leg = 2mn = 2(3)(2) = 12
Now, we can check whether 13, 5, 12 be the three sides of the right angle triangle using Pythagorean theorem.
That is,
square of hypotenuse = sum of the squares of other sides
13² = 5² + 12²
169 = 25 + 144
169 = 169
In this way, we will be able to create the lengths of three sides of a right triangle using the formulas given above.
Some more examples
Example 1 :
Using 5 and 6, create the lengths of three sides of a right triangle.
Solution :
Since m > n, we can take m = 6 and n = 5
Then, we have
Hypotenuse = m² + n² = 6² + 5² = 36 + 25 = 61
Leg = m² - n² = 6² - 5² = 36 - 25 = 11
Leg = 2mn = 2(6)(5) = 60
Hence, the lengths of three sides of the right triangle are
61, 11 and 60
Let us look at the next example on "Pythagorean triple generator"
Example 2 :
Using 4 and 3, create the lengths of three sides of a right triangle.
Solution :
Since m > n, we can take m = 4 and n = 3
Then, we have
Hypotenuse = m² + n² = 4² + 3² = 16 + 9 = 25
Leg = m² - n² = 4² - 3² = 16 - 9 = 7
Leg = 2mn = 2(4)(3) = 24
Hence, the lengths of three sides of the right triangle are
25, 7 and 24
Let us look at the next example on "Pythagorean triple generator"
Example 3 :
Using 1 and 2, create the lengths of three sides of a right triangle.
Solution :
Since m > n, we can take m = 2 and n = 1
Then, we have
Hypotenuse = m² + n² = 2² + 1² = 4 + 1 = 5
Leg = m² - n² = 2² - 1² = 4 - 1 = 3
Leg = 2mn = 2(2)(1) = 4
Hence, the lengths of three sides of the right triangle are
5, 3 and 4
Let us look at the next example on "Pythagorean triple generator"
Example 4 :
Using 6 and 7, create the lengths of three sides of a right triangle.
Solution :
Since m > n, we can take m = 7 and n = 6
Then, we have
Hypotenuse = m² + n² = 7² + 6² = 49 + 36 = 85
Leg = m² - n² = 7² - 6² = 49 - 36 = 13
Leg = 2mn = 2(7)(6) = 84
Hence, the lengths of three sides of the right triangle are
85, 13 and 84
Let us look at the next example on "Pythagorean triple generator"
Example 5 :
Using 11 and 6, create the lengths of three sides of a right triangle.
Solution :
Since m > n, we can take m = 11 and n = 6
Then, we have
Hypotenuse = m² + n² = 11² + 6² = 121 + 36 = 157
Leg = m² - n² = 11² - 6² = 121 - 36 = 85
Leg = 2mn = 2(11)(5) = 110
Hence, the lengths of three sides of the right triangle are
157, 85 and 110
After having gone through the stuff, we hope that the students would have understood "Pythagorean triple generator".
Apart from the stuff "Pythagorean triple generator"given on this web page, If you need some other stuff in math please use our custom search here.
WORD PROBLEMS
HCF and LCM word problems
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
Sum of all three four digit numbers formed using 0, 1, 2, 3
Sum of all three four digit numbers formed using 1, 2, 5, 6
