QUESTION 2/10 Trueorfalse? There exists noequilateral righttriangle (a right :trianglewhere all sides are the same length). 1 point True False

## Step 1<br />The problem is asking whether there exists an equilateral right triangle. An equilateral triangle is a triangle where all sides are of equal length. A right triangle, on the other hand, is a triangle where one of the angles is 90 degrees.<br /><br />## Step 2<br />The Pythagorean theorem is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that 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 \(a\) and \(b\) are the lengths of the two legs of the right triangle, and \(c\) is the length of the hypotenuse.<br /><br />## Step 3<br />If we try to apply this theorem to an equilateral triangle, where all sides are of equal length, we would have \(a = b = c\). Substituting these values into the Pythagorean theorem, we get:<br />### \(a^2 + a^2 = a^2\)<br />which simplifies to:<br />### \(2a^2 = a^2\)<br /><br />## Step 4<br />This equation is not possible for any real number \(a\), which means that an equilateral triangle cannot be a right triangle.