Q. 56 - Precalculus Enhanced with Graphing Utilities

Question

The length of fence required to enclose a rectangular field is 3000 meters. What are the dimensions of the field if it is known that the difference between its length and width is 50 meters?

Step-by-Step Solution

Answer

The length and breadth of rectangle is 775meters and 725meters

Step 1: Given information

We are given that the length of fence required to enclose a rectangular field is 3000 meters also the difference between length and breadth is 50 meters

Step 2: Find the equation and solve them

Let $$\begin{gathered} l=length \\ b=breadth \end{gathered}$$

The length of fence required to enclose a rectangular field is 3000 meters 

Hence

$$\begin{gathered} P=2(l+b) \\ 3000=2(l+b) \\ l+b=1500 \left(1\right) \end{gathered}$$

Also the difference between length and breadth is 50 meters is

$l-b=50 \left(2\right)$

Now we add equation 1 and 2

We get,

$l+b=1500+l-b=502l=1550$

Hence $l=775meter$

Now we find the breadth

$$\begin{gathered} l-b=50 \\ b=l-50 \\ b=775-50 \\ b=725meters \end{gathered}$$

Step 3: Conclusion

The length and breadth of rectangle is 775 meters and 725 meters