Answer:
28 yards.
Explanation:
We can use the formula for the area of a right triangle to find the length of the longest side (the hypotenuse) of the playground. The area of a right triangle is given by:
A = 1/2 * base * height
where the base and height are the lengths of the two legs of the right triangle.
In this case, the area of the playground is given as 294 yards, and one of the legs (the short side) is given as 21 yards. Let x be the length of the longest side (the hypotenuse) of the playground. Then, we can write:
294 = 1/2 * 21 * x
Multiplying both sides by 2 and dividing by 21, we get:
x = 2 * 294 / 21
Simplifying the expression on the right-hand side, we get:
x = 28
Therefore, the length of the path along the longest side (the hypotenuse) of the playground would be 28 yards.