Question

please show work A flower garden is in the shape of a right triangle. The longest side of the triangle measures 13 m. One of the shorter sides is 7 m longer than the other. Determine the length of the shortest side

Answer 1

To find the length of the shortest side of the right triangle, we can use the Pythagorean Theorem. Let the shortest side be x and the longer side be x + 7. Using the theorem, we have x^2 + (x + 7)^2 = 13^2. Solving this quadratic equation, we find that x = 5. Therefore, the length of the shortest side is 5 meters.

Step-by-step explanation:

To find the length of the shortest side of the right triangle, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. Let the shortest side be x, and the longer side be x + 7. Using the theorem, we have x^2 + (x + 7)^2 = 13^2. Expanding this equation and simplifying, we get 2x^2 + 14x - 120 = 0. Solving this quadratic equation, we find that x = 5. Therefore, the length of the shortest side is 5 meters.