Chapter 9.8, Problem 3P

To determine

To calculate: To find the dimensions of the property

Answer to Problem 3P

Length of rectangular property is $43$ m and width is $35$ m

Explanation of Solution

Given information: The fence around a rectangular piece of property is $156$ m long and the area of property is $1505m^2$

Calculation:

Let the length and width of rectangular property be $x$ and $y$ respectively

Given that the fence around a rectangular piece of property is $156$ m long and the area of property is $1505m^2$

Thus, equations are given as follows:

  $\begin{array}{l}2\left(x+y\right)=156----(1)\\ xy=1505------(2)\end{array}$

From equation (2),

  $y=\frac{1505}{x}$

Substituting the value in equation (2)

  $\begin{array}{l}2\left(x+y\right)=156\\ x+y=78\\ x+\frac{1505}{x}=78\\ x^2+1505=78x\\ x^2-78x+1505=0\\ \left(x-43\right)\left(x-35\right)=0\\ x=45,35\end{array}$

When $x=43$

  $\begin{array}{l}y=\frac{1505}{43}\\ y=35\end{array}$

When $x=35$

  $\begin{array}{l}y=\frac{1505}{35}\\ y=43\end{array}$

Conclusion:

Hence, length of rectangular property is $43$ m and width is $35$ m