The length of a rectangular garden is 26 yards and a pathway that runs diagonally through the garden is 75 yards long. What is the width of the garden?

To find the width of the garden, you can apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (in this case, the diagonal pathway) is equal to the sum of the squares of the lengths of the other two sides (the length and the width of the garden). Here, you have the equation: \( 26^2 + w^2 = 75^2 \). Calculating this yields \( 676 + w^2 = 5625 \). Subtracting 676 from both sides gives you \( w^2 = 4949 \). To find \( w \), you take the square root, leading to a width of approximately 70.4 yards. Voila! Your garden is in good shape! Additionally, gardening enthusiasts often find that having a well-planned layout enhances both beauty and functionality. Consider designing specific zones like vegetable patches or flower beds to maximize your space and add personality! If you're keen on tackling such problems further, why not dive into some geometry textbooks or online resources? They can offer more complex scenarios and exercises to sharpen your skills while perhaps even revealing the underlying relationships in shapes that can transform your garden's appeal!