A disoriented driver crosses diagonally from one corner of a 150 m by 275 m lawn to the far corner. How far does the wayward driver drive across the lawn? Give an approximate answer to three decimal places.

To find out how far the disoriented driver drives across the lawn, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the lawn forms a right triangle, with one side measuring 150 m and the other side measuring 275 m. The hypotenuse represents the path the driver takes across the lawn.

So, using the Pythagorean theorem, we can calculate the length of the hypotenuse (the distance the driver drives):

Hypotenuse^2 = length of one side^2 + length of the other side^2
= 150^2 + 275^2

Now, we can calculate the length of the hypotenuse:

Hypotenuse = √(150^2 + 275^2)

Using a calculator, we find that:

Hypotenuse ≈ 315.366

Therefore, the disoriented driver drives approximately 315.366 meters across the lawn.