The hypotenuse of a right triangle is √61. What whole-number lengths of legs can this triangle have? Explain.
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Do u have Canadian math book
To determine the whole-number lengths of the legs of a right triangle when the length of the hypotenuse is given, you 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 two legs.
Let's call the lengths of the legs a and b, and the hypotenuse c. The Pythagorean theorem can be written as:
a^2 + b^2 = c^2
In this case, we are given that the hypotenuse (c) is √61. We need to find the whole-number lengths of the legs (a and b).
We can square both sides of the equation to solve for the legs:
a^2 + b^2 = (√61)^2
a^2 + b^2 = 61
Now, we need to find possible combinations of whole numbers (a and b) that satisfy the equation a^2 + b^2 = 61.
Start by considering possible values for one leg of the triangle, let's say a. Since a is a whole number, it can be any whole number from 1 upwards.
Calculate the corresponding value of b using the equation b = √(61 - a^2). This formula comes from rearranging a^2 + b^2 = 61 to solve for b.
Compute the value of b for each possible value of a. If b is a whole number, then the pair (a, b) is a valid set of whole-number lengths for the legs of the right triangle.
For example, if you start with a = 1, calculate b: b = √(61 - 1^2) = √60. Since √60 is not a whole number, (1, √60) is not a valid solution.
Continue this process by incrementing the value of a and calculating the corresponding value of b until you find all the valid sets of whole-number lengths for the legs of the right triangle.
By following this method, you will be able to determine the whole-number lengths of the legs of the triangle.
x^2 + y^2 = 61
x x^2 y^2
1 1 == 60 nope
2 4 == 57 nope
3 9 == 52 nope
4 16 = 45 nope
5 25 = 36 SCORE!!! 5 and 6
6 36 well then 25 of course
7 49 = 12 nope
8 too big