The length of the hypotenuse (x) is an irrational number between 6 and 8. Both legs have measures that are whole numbers. Illustrate a model for at least one possible set of measures for the sides of the right triangle.
4^2 + 5^2 = 41
I dont want the answer i wanna learn how to do it so I don't have to depend on other people
omg so thats the formula?
Tytytyty
just try
hypotenuse squared between
x^2+y^2 = 36
to
x^2 + y^2 = 64
for example try 3 and something
3^2 + 7^2 = 58, that works sqrt 58 = 7.615 ..... etc
the square of the hypotenuse is between 36 and 64 ... 6^2 and 8^2
from Pythagoras ... a^2 + b^2 = c^2
so the sum of the squares of the two legs is more than 36 and less than 64
you are looking for pairs of whole numbers with the correct sum of squares
... as the question indicates , there are multiple possibilities
Can you please explain
I still dont understand so i try a number between 7 and 8 to try and find the other ones?
To find a possible set of measures for the sides of the right triangle with a hypotenuse, "x," between 6 and 8, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's assume that one of the legs of the triangle has a length of "a" and the other leg length of "b." We can set up the equation as:
a^2 + b^2 = x^2
Since both legs have measures that are whole numbers, we can start by trying out different combinations of whole numbers for one of the legs and see if it satisfies the equation.
For example, let's assume "a" is 3. Plugging it into the equation, we get:
3^2 + b^2 = x^2
9 + b^2 = x^2
Next, we need to check the possible values of "b" that satisfy the equation. We know that the hypotenuse, "x," is an irrational number between 6 and 8. Therefore, the square of "x" will also be an irrational number between 36 and 64.
Let's choose a value for "x" within that range, say 6.5. Plugging it into the equation, we get:
9 + b^2 = 6.5^2
9 + b^2 = 42.25
Now, we can solve for "b" by subtracting 9 from both sides:
b^2 = 42.25 - 9
b^2 = 33.25
Taking the square root of both sides, we find:
b ≈ √33.25
b ≈ 5.771
Since both legs have measures that are whole numbers, the value of "b" is not a whole number in this case. Therefore, we need to repeat the process with different values for "a" and "x" until we find a set of measures that satisfy all the conditions.
By repeating this process with different values, you can eventually find a set of measures for the sides of the right triangle that satisfies the given conditions. However, it's important to note that there might be multiple solutions, and further calculation would be necessary to find alternative sets of measures.