Question

A playground is in the shape of a right triangle with an area of 294 yd^2. The shortest side of the playground (one of the legs) is 21 yds. The city council would like to add a path along the longest side of the playground (the hypotenuse). How long would the path be?

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Answer 1

35 yards.

Explanation:

We can use the Pythagorean theorem to solve this problem. Let's call the other leg of the triangle "x" and the length of the hypotenuse (the path the council would like to add) "c". Then we have:

Area of triangle = (1/2) * base * height

294 = (1/2) * 21 * x

x = 28

Now we can use the Pythagorean theorem to find "c":

c^2 = 21^2 + 28^2

c^2 = 441 + 784

c^2 = 1225

c = sqrt(1225)

c = 35

So the length of the path the council would like to add is 35 yards.

Answer 2

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.