Isis possible for a right triangle to have side tengths 16,30, and 34? 16,30, 1 point Yes, it is possible. No,itisnot possible. Cannot bedetermined.

## Step 1<br />The problem involves the Pythagorean theorem, which states that in a right 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. This can be written as:<br />### \(a^2 + b^2 = c^2\)<br />where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two sides.<br /><br />## Step 2<br />In this problem, the given side lengths are 16, 30, and 34. We need to check if these lengths satisfy the Pythagorean theorem.<br /><br />## Step 3<br />We calculate the squares of the given side lengths:<br />### \(16^2 = 256\)<br />### \(30^2 = 900\)<br />### \(34^2 = 1156\)<br /><br />## Step 4<br />We then add the squares of the two smaller side lengths:<br />### \(256 + 900 = 1156\)<br /><br />## Step 5<br />We compare this sum with the square of the longest side length:<br />### \(1156 = 1156\)<br /><br />Since the sum of the squares of the two smaller side lengths equals the square of the longest side length, the given side lengths satisfy the Pythagorean theorem.