Question

what is the length of the rectangular plot of land shown? How are the lengths of the legs of a right triangle related to the lengths of the sides of a right rectangle?The length of the rectangular plot of land is _______ ft.

Answer 1

The length of the rectangular plot of land is;

`125\text{ ft}`

Step-by-step explanation:

Given the figure in the attached.

The diagonal length of the rectangle is given as;

`c=325\text{ ft}`

The width of the rectangle is given as;

`w=300\text{ ft}`

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.

`\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}`

Substituting the given values;

`\begin{gathered} l=\sqrt[]{325^2-300^2} \\ l=\sqrt[]{15625} \\ l=125\text{ ft} \end{gathered}`

Therefore, the length of the rectangular plot of land is;

`125\text{ ft}`