Question

a rectangular plot of land is designed so that its length is 2 meters more than its width. the diagonal of the land is 16 meters. to the nearest tenth of a meter, what are the dimensions of the land? the width of the land is meters and the length of the land is meters (round to the nearest tenth as needed)

Explanation:

Step1: Define variables

Let width = \( w \), length = \( w + 2 \)

Step2: Apply Pythagorean theorem

\( w^2 + (w + 2)^2 = 16^2 \)

Step3: Expand and simplify

\( 2w^2 + 4w - 252 = 0 \Rightarrow w^2 + 2w - 126 = 0 \)

Step4: Solve quadratic equation

\( w = \frac{-2 + \sqrt{4 + 504}}{2} \approx 10.3 \)

Step5: Find length

Length = \( 10.3 + 2 = 12.3 \)

Answer:

10.3, 12.3