6. Alena designed an obstacle course. On the course, there is a ladder leaning against the top of a 24 ft wall. If the ladder is 7 ft from the base of the wall, then what is the length of the ladder? 25 feet 15.5 feet 31 feet feet

To find the length of the ladder, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the ladder) is equal to the sum of the squares of the other two sides (the wall and the distance from the wall). Here, we have a wall of 24 ft and a horizontal distance of 7 ft. Using the formula: \( c^2 = a^2 + b^2 \), we can set \( a = 24 \) ft and \( b = 7 \) ft. Calculating: \( c^2 = 24^2 + 7^2 = 576 + 49 = 625 \). Taking the square root yields \( c = \sqrt{625} = 25 \) feet. So, the length of the ladder is 25 feet! Ever thought about how the Pythagorean theorem came to be? It’s over 2500 years old and attributed to the Greek mathematician Pythagoras. The theorem is not just for ladders and walls; it’s used in everything from architecture to navigation! Pythagorean triples, such as (3, 4, 5) or (5, 12, 13), are whole-number solutions to the theorem—perfect for those geometry quizzes! If you find yourself grappling with similar problems in the future, remember to always sketch the scenario. Draw the triangle formed, label your sides, and apply the Pythagorean theorem carefully. A common mistake is mixing up the legs of the triangle — just remember the hypotenuse is always the side opposite the right angle and the longest side in your case. Happy problem-solving!