Use Pythagorean Theorem to determine which set of sides can be the sides of a right triangle.
Question 14 options:
a) 3,4,5
b) 4,4,8
c) 6,6,12
d) 8,9,10
To determine which set of sides can be the sides of a right triangle using the Pythagorean Theorem, we need to check if the squares of the two shorter sides add up to the square of the longest side.
Let's go through each option:
a) 3, 4, 5
Using the Pythagorean Theorem:
3^2 + 4^2 = 9 + 16 = 25
5^2 = 25
Since the squares of the two shorter sides (3 and 4) add up to the square of the longest side (5), this set of sides can be the sides of a right triangle.
b) 4, 4, 8
Using the Pythagorean Theorem:
4^2 + 4^2 = 16 + 16 = 32
8^2 = 64
The squares of the two shorter sides (4 and 4) do not add up to the square of the longest side (8), so this set of sides cannot be the sides of a right triangle.
c) 6, 6, 12
Using the Pythagorean Theorem:
6^2 + 6^2 = 36 + 36 = 72
12^2 = 144
The squares of the two shorter sides (6 and 6) do not add up to the square of the longest side (12), so this set of sides cannot be the sides of a right triangle.
d) 8, 9, 10
Using the Pythagorean Theorem:
8^2 + 9^2 = 64 + 81 = 145
10^2 = 100
The squares of the two shorter sides (8 and 9) do not add up to the square of the longest side (10), so this set of sides cannot be the sides of a right triangle.
Therefore, the correct answer is option a) 3, 4, 5.
To determine which set of sides can form a right triangle using the Pythagorean theorem, we need to check if the sum of the squares of the two shorter sides is equal to the square of the longest side.
Let's calculate the squares of the sides of each option:
a) For the set of sides 3, 4, 5:
3^2 + 4^2 = 9 + 16 = 25
5^2 = 25
b) For the set of sides 4, 4, 8:
4^2 + 4^2 = 16 + 16 = 32
8^2 = 64
c) For the set of sides 6, 6, 12:
6^2 + 6^2 = 36 + 36 = 72
12^2 = 144
d) For the set of sides 8, 9, 10:
8^2 + 9^2 = 64 + 81 = 145
10^2 = 100
From the calculations above, we can see that only option a) satisfies the Pythagorean theorem since the sum of the squares of the two shorter sides (3^2 + 4^2 = 25) is equal to the square of the longest side (5^2 = 25). Therefore, option a) (3, 4, 5) can be the sides of a right triangle.
Recall the Pythagorean theorem:
c^2 = a^2 + b^2
where c is the hypotenuse (which is also the longest side of a right triangle) and a & b are the legs.
Substitute each side lengths to the equation. Of course the longest side is c, and the remaining sides are a and b. If the set of side lengths satisfies the pythagorean equation, therefore, it is a right triangle.
Hope this helps~ :3