Question

A small city park is in the shape of a right triangle with an area of 294 yd². The shortest side of the park (one

of the legs) is 21 yds. The city council would like to add a path along the longest side of the park (the
hypotenuse). How long would the path be? Show your work. Don’t forget to label your answer. See page

Answer 1

To solve this problem, we can use the Pythagorean theorem, which states that for any right triangle with legs of length a and b and hypotenuse of length c, a² + b² = c².

We are given that one of the legs has a length of 21 yds, and the area of the park is 294 yd². We can use the area formula for a right triangle to find the length of the other leg:

area = 1/2 * base * height

294 = 1/2 * 21 * height

294 = 10.5 * height

height = 28

So the other leg has a length of 28 yds. Now we can use the Pythagorean theorem to find the length of the hypotenuse:

c² = a² + b²

c² = 21² + 28²

c² = 441 + 784

c² = 1225

c = √1225

c = 35

Therefore, the length of the path along the longest side of the park would be 35 yds