Question

A 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.

Answer 1

Answer: The length of the path along the longest side of the park would be 35 yds.

Step-by-step explanation: Area of triangle = (1/2) x base x height294 = (1/2) x 21 x heightMultiplying both sides by 2 and dividing by 21, we get:height = 28So the other leg of the triangle is 28 yds.Now we can use the Pythagorean theorem to find the length of the hypotenuse:hypotenuse² = shortest side² + other leg²hypotenuse² = 21² + 28²hypotenuse² = 441 + 784hypotenuse² = 1225Taking the square root of both sides, we get:hypotenuse = 35Therefore, the length of the path along the longest side of the park would be 35 yds.