For exercises \( 9-14 \), answer the questions. 9. An isosceles right triangle has legs that are 3 units long. What is the length of the hypotenuse of the triangle? \( \begin{array}{lll}\text { A. } 3 \text { units } & \text { B. } \sqrt{18} \text { units } & \text { C. } 9 \text { units }\end{array} \) D. 18 units 10. A right triangle has a hypotenuse that is 5 units long. One of the legs of the triangle is 4 units long. What is the length of the other leg of the triangle?

The length of the hypotenuse of an isosceles right triangle can be found using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). For an isosceles triangle where both legs are equal, we have \( a = b = 3 \). So, \( c^2 = 3^2 + 3^2 = 9 + 9 = 18 \). Therefore, \( c = \sqrt{18} \) units, which simplifies to \( 3\sqrt{2} \) units. To find the length of the other leg of a right triangle when one leg and the hypotenuse are known, we again apply the Pythagorean theorem. Given that one leg \( a = 4 \) and the hypotenuse \( c = 5 \), we can set it up as \( c^2 = a^2 + b^2 \). Plugging in the values gives \( 5^2 = 4^2 + b^2 \), or \( 25 = 16 + b^2 \). Solving this, we find \( b^2 = 9 \), which means \( b = 3 \) units.