The sides of a triangle are 88, 65, and 68. Use the Pythagorean Theorem to determine if the triangle is right,acute, or obtuse. Answer Attemptiout of The triangle is square because the square of the largest side square the sum of the squares of the other two sides.

## Step 1<br />The Pythagorean Theorem states that in a right-angled 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. This can be written as:<br />### \(a^2 + b^2 = c^2\)<br />where \(c\) is the hypotenuse and \(a\) and \(b\) are the other two sides.<br /><br />## Step 2<br />In this problem, the sides of the triangle are 88, 65, and 68. The largest side is 88, so we will consider this as the hypotenuse.<br /><br />## Step 3<br />We need to check if the square of the largest side is equal to the sum of the squares of the other two sides. If it is, the triangle is right-angled. If the square of the largest side is greater than the sum of the squares of the other two sides, the triangle is obtuse. If the square of the largest side is less than the sum of the squares of the other two sides, the triangle is acute.<br /><br />## Step 4<br />Let's calculate:<br />### \(88^2 = 7744\)<br />### \(65^2 + 68^2 = 4225 + 4624 = 8849\)<br /><br />## Step 5<br />Since \(7744 < 8849\), the triangle is acute.