Mr. Grant has a tree farm in the shape of a square. Half the farm has trees that he uses to make pencils and the other half are maple trees that he uses to make maple syrup.

Question

The farm is divided into two equal sections along a 400-foot diagonal as shown. What is the length of one side of the tree farm? Represent your answer in the simplest radical form and provide the decimal form to the nearest tenth.

Answer 1

The diagonal of a square is the side times the square root of 2.

You figure the answer from this hint.

Answer 2

400/sqr2 = 400sqr2/2 = 200sqr2 feet

=about 400(1.414)/2 = about 200(1.414) = 282.8 feet

by the Pythagorean Theorem

400^2 = s^2 + s^2 = 2s^2

s^2 = 400^2/2

s = 400/sqr2 = 400sqr2/2 = 200sqr2 = about 282.8 feet