Hello! I'm stuck on Pythagorean theorem in basic geometry in math. This is the question.Which side lengths form a right triangle?
Choose all answers that apply:
A. 3, v``9`, v``18`
B. 3,4,5
C. 7,7, v``98`
I don't know how to make the line at the top so I just put this ` instead.
The Pythagorean Theorem states that for a right triangle with sides a and b, and hypotenuse c,
a^2 + b^2 = c^2
So, you just need to check to see which numbers obey that equation.
Does 3^2 + 9^2 = 18^2 ?
9 + 81 = 324?
I think not.
There are a lot of these geometry questions that I need help with. Especially with Pythagorean theorem questions like this.
Hello! I can help you understand and solve this question about the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
To find out which side lengths form a right triangle, we need to check if the Pythagorean theorem holds true for each set of side lengths.
Let's go through each option:
A. 3, v``9`, v``18`
To check if these side lengths form a right triangle, apply the Pythagorean theorem:
- If the largest side is `v18`, the other two sides must be `3` and `v9`.
- Plugging these values into the Pythagorean theorem: `3^2 + v9^2 = v18^2`
- Simplifying: `9 + 9 = 18`
- This equation is not true, so the side lengths `3`, `v9`, and `v18` do not form a right triangle.
B. 3, 4, 5
To check if these side lengths form a right triangle:
- The largest side is `5`, and the other two sides are `3` and `4`.
- Applying the Pythagorean theorem: `3^2 + 4^2 = 5^2`
- Simplifying: `9 + 16 = 25`
- This equation is true, so the side lengths `3`, `4`, and `5` form a right triangle.
C. 7, 7, v``98`
To check if these side lengths form a right triangle:
- The largest side is `v98`, and the other two sides are both `7`.
- Applying the Pythagorean theorem: `7^2 + 7^2 = v98^2`
- Simplifying: `49 + 49 = 98`
- This equation is true, so the side lengths `7`, `7`, and `v98` form a right triangle.
Based on the analysis, the side lengths that form a right triangle are:
B. 3, 4, 5
C. 7, 7, v``98`
I hope this explanation helps you understand how to determine which side lengths form a right triangle using the Pythagorean theorem! If you have any further questions, feel free to ask.