Answer:
Answer: The length of the path would be 35 yds.
Explanation:
We can use the formula for the area of a right triangle to find the length of the other leg. Once we know the lengths of both legs, we can use the Pythagorean theorem to find the length of the hypotenuse.
Let's call the length of the shortest side (the leg) "a", and let's call the length of the other side (the other leg) "b". We know that a = 21 yd and the area of the triangle is 294 yd^2. So we can use the formula for the area of a right triangle to solve for b:
area = (1/2) * a * b
294 = (1/2) * 21 * b
b = (2 * 294) / 21
b = 28
Now we know that a = 21 yd and b = 28 yd. We can use the Pythagorean theorem to find the length of the hypotenuse (c):
c^2 = a^2 + b^2
c^2 = 21^2 + 28^2
c^2 = 441 + 784
c^2 = 1225
c = sqrt(1225)
c = 35
Therefore, the length of the path along the longest side of the playground would be 35 yds.