The diagonal length of a square is 14.1 sq. units. What is the area of

If a is the length of a side of the square, then a diagonal divides the square into two congruent (equal) right
triangles. Applying The Pythagorean Theorem to either triangle yields diagonal^2 = side^2 + side2^ = a^2 + a^2 =
2a^2. Taking the square root of both sides of this equation yields diagonal = a 2 . We are given that the
diagonal length is 14.1. Hence, a*sqrt(2) = 14.1 or a = 14.1/sqrt(2)

Now, the area, a^2, equals [14.1/sqrt(2)]^2 ==> 14.1^2 / 2

==> 198.81/2 => 99.4

The number 99.4 is nearest to 99. Hence, the answer is (D).

Note: If you had approximated 14.1/sqrt(2) with 10, you would have mistakenly gotten 100 and would have
answered (E). Approximation is the culprit. Prefer doing it in the last.

This problem was from Nova's Math Bible