Chapter 7.2, Problem 5P

To determine

To find: The dimensions of the field.

Answer to Problem 5P

The dimension of the rectangular field is 100 m and 50m.

Explanation of Solution

Given:

The area of the rectangular field = 5000 m².

The length of the fencing of the rectangular field = 300 m

Calculation:

The area of the rectangle is given by

  $\begin{array}{l}A=l\times b\\ \text{Here, }l\text{is the length of the rectangle and }b\text{ is the bredth of the rectangle}\text{.}\end{array}$

The initial area of the rectangle

  $\begin{array}{l}{A}_1=5000{\text{m}}^2\\ 5000=l\times b\end{array}$

The length of the fencing of the rectangular field will be equal to the perimeter of the rectangular field.

The perimeter of the rectangle is given by

  $\begin{array}{l}P=2\left(l+b\right)\\ 300=2\times \left(l+b\right)\\ l+b=150\end{array}$

Substitute $b=\frac{5000}{l}$ in the above equation.

  $\begin{array}{l}l+\frac{5000}{l}=150\\ l^2-150l+5000=0\\ l^2-100l-50l+5000=0\\ l\left(l-100\right)-50\left(l-100\right)=0\\ \left(l-100\right)\left(l-50\right)=0\\ l=100\\ l=50\end{array}$

And

The breadth of the rectangle

  $\begin{array}{l}b=\frac{5000}{100}=50\\ b=\frac{5000}{50}=100\end{array}$

The dimension of the rectangular field is 100 m and 50m.

Therefore, the dimension of the rectangular field is 100 m and 50m.

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