Answer:
The length of the rectangular plot of land is;
[tex]125\text{ ft}[/tex]
Explanation:
Given the figure in the attached.
The diagonal length of the rectangle is given as;
[tex]c=325\text{ ft}[/tex]
The width of the rectangle is given as;
[tex]w=300\text{ ft}[/tex]
The diagonals, width and the length of the rectangle forms a right angled triangle.
So, the length of any of the legs can be calculated using Pythagorean theorem.
with the diagonal as the hypotenuse.
[tex]\begin{gathered} c^2=a^2+b^2 \\ c^2=w^2+l^2 \\ l^2=c^2-w^2 \\ l=\sqrt[]{c^2-w^2} \end{gathered}[/tex]
Substituting the given values;
[tex]\begin{gathered} l=\sqrt[]{325^2-300^2} \\ l=\sqrt[]{15625} \\ l=125\text{ ft} \end{gathered}[/tex]
Therefore, the length of the rectangular plot of land is;
[tex]125\text{ ft}[/tex]
