A right triangle has two sides equal to 8
units and 17
units. Which could be the length of the third side of this triangle?
Responses
5
units
5 units
9
units
9 units
15
units
15 units
21
units
The length of the third side of a right triangle can be found using the Pythagorean theorem, which states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Let's use this theorem to find the length of the third side:
Using the Pythagorean theorem:
8^2 + 17^2 = c^2
64 + 289 = c^2
353 = c^2
To find the length of the third side, we need to take the square root of both sides:
√353 = √c^2
√353 = c
The options given are:
5 units
9 units
15 units
21 units
After taking the square root of 353, the length of the third side is approximately 18.8 units. Therefore, none of the given options match the length of the third side of this triangle.
To find the length of the third side of a right triangle, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we have two sides equal to 8 units and 17 units. Let's label the sides as side A, side B, and side C, where side C is the third side that we are trying to find.
Using the Pythagorean theorem:
A^2 + B^2 = C^2
Substituting the known values:
8^2 + 17^2 = C^2
64 + 289 = C^2
353 = C^2
To find the value of C, we need to take the square root of both sides:
√353 ≈ 18.79
So, the length of the third side could be approximately 18.79 units.
Among the given options, none of them matches the calculated value of approximately 18.79 units.
To find the length of the third side of a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the two sides are 8 units and 17 units. Let's check which of the given options satisfy this condition.
Option 1: Length of the third side = 5 units
Using the Pythagorean theorem, 8^2 + 17^2 = 5^2
64 + 289 ≠ 25
Option 2: Length of the third side = 9 units
Using the Pythagorean theorem, 8^2 + 17^2 = 9^2
64 + 289 ≠ 81
Option 3: Length of the third side = 15 units
Using the Pythagorean theorem, 8^2 + 17^2 = 15^2
64 + 289 = 225
Option 4: Length of the third side = 21 units
Using the Pythagorean theorem, 8^2 + 17^2 = 21^2
64 + 289 ≠ 441
Therefore, the length of the third side that satisfies the conditions is 15 units.