To find the area of a rectangular park, one can use the formula:.Area=length×width. In this case, the dimensions of the park are given as 20 yards, 30 yards, and 40 yards for the length, width, and diagonal, respectively.
Firstly, it's important to recognize that the length, width, and diagonal of the park form a right-angled triangle. The diagonal serves as the hypotenuse, and the length and width are the legs. According to the Pythagorean theorem, in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): c²=a²+b².
In this scenario, the Pythagorean theorem can be applied to find the length and width of the park. Given that the diagonal (c) is 40 yards, and the length (a) and width (b) are 20 and 30 yards (in some order), we can substitute these values into the theorem to determine the correct pairing.
40²=20²+30².
Solving for a and b, we find a=10 and b=30. Therefore, the length of the park is 20 yards, the width is 30 yards, and the diagonal is 40 yards.
Now, we can use the formula for the area: Area=length×width=20×30=600 square yards.
In conclusion, the area of the park is 600 square yards, and this calculation involves both the Pythagorean theorem and the fundamental formula for the area of a rectangle.