Answer:
No, because the given values do not produce a correct equation when plugged into the Pythagorean Theorem.
Explanation:
To solve this question, we can use the Pythagorean Theorem. (Also called Pythagoras Theorem)
The Pythagorean Theorem is true for ALL right triangles, meaning that if the side lengths don't work for it, the given triangle can not be a right triangle.
The theorem simply states that the sum of the squares of the two legs must add up to the square of the hypotenuse.
Note that the hypotenuse of a triangle is the side opposite to the right angle.
The Pythagorean Theorem can be easily written as the following expression:
a^2+b^2=c^2
This is where a and b are the legs and c is the hypotenuse.
We can plug our given values in to see if it's correct.
If it is a right triangle, the longest side will always be the hypotenuse, so we can safely set c as 13.
4^2+10^2=13^2
Simplify to see if it's true
16+100=169
116≠169
Therefore, a right triangle can not have these given side lengths.
Hope that helps, please let me know if you have any further questions!