Question

Find the value of x. Then tell whether the side lengths form a Pythagorean triple.
10, 6​

Answer 1

To find the value of x using the sides 6 and 10, apply the Pythagorean theorem: x = √(6² + 10²), which results in x = 11.66. These side lengths do not form a Pythagorean triple because 11.66 is not a whole number.

Step-by-step explanation:

To find the value of x, when given two sides of a right triangle, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b), which can be expressed as c² = a² + b². To solve for x, the missing hypotenuse, we use the formula c = √(a² + b²).

If we are given that one side (a) is 6 and the other side (b) is 10, we can calculate:
x = √(6² + 10²)
x = √(36 + 100)
x = √136
x = 11.66 (to two decimal places)

To determine whether these side lengths form a Pythagorean triple, all the side lengths a, b, and c must be whole numbers when squared and added together. Since 11.66 is not a whole number, the lengths 6, 10, and 11.66 do not form a Pythagorean triple.

Answer 2

To Find :

The value of x.

Solution :

Applying Pythagoras's theorem by assuming 10 is the biggest side, we get :

`6^2 + x^2 = 10^2\\\\x = √(100 - 36)\\\\x = √(64)\\\\x = 8`

Therefore, the value of x is 8 .