Question

Chile plans to add about 40,404 square kilometers of national parkland. Suppose a single piece of land is 40,404 square kilometers and is shaped like a square. What is the length of a diagonal of the square to the nearest kilometer?

284 km
201 km
402 km
571 km

Answer 1

The length of the diagonal is 284 km

Step-by-step explanation:

1- we get the side length of the side:

We are given that the land has a square shape and an area of 40,404 km²

Area of square = (side)²

40,404 = (side)²

side = +√40,404

side = 201.007 km ≈ 201 km

2- we get the length of the diagonal:

Refer to the attach picture representing the area of land.

We can infer that the two side lengths along with the diagonal of the land form a right-angled triangle.

Therefore, to get the diagonal, we can apply the Pythagorean theorem as follows:

`Diagonal = √((201)^2+(201)^2)`

Diagonal = 284.2 ≈ 284 km

Hope this helps :)