Official Explanation

RO1

The sides of the plot’s boundary that form the right angle of the triangle are 2 km and b km long, and the longest side is c km long. Using the Pythagorean Theorem, \(c^2 = 2^2 + b^2 = 4 + b^2.\) Taking the square root of each side gives \(\sqrt{4+b^2}\). The area of the triangle, A km, can be found using the equation \(\frac{1}{2}(base)(height).\)\(=\frac{1}{2}(b)(2)\) Since A = b, A can be substituted into the previous expression: \(c=\sqrt{4+A^2}\). Using this equation, the value of c can be calculated for each possible value of A. The table below shows the calculations, rounded to the nearest tenth:


The only one of these values of c that is among the options given is 2.8.

The correct answer is 2.8.

RO2

As shown in the table provided in the analysis for RO1, c = 2.8 corresponds to A = 2.0.

The correct answer is 2.0.