Farmer Joe has a rectangular pen to hold his animals. The pen’s length is 5 meters longer than the width. The pen’s area is 84 meters. Find it’s width.

Step 1 define the variables:

L stands for the length, W stands for the width

Step 2 write what we know algebraically: 

Since the length is 5 meters longer than the width we have L = W + 5.

Finally, the area is 84 meters so we have that 84 = W*L

Step 3 Solve :

Let’s first plug L = W + 5 into our Area equation to get 84 = W*(W+5) = W² + 5W  which is the same as saying 

0 = W² +5W - 84. Solving the quadratic equation we get 0 = (W - 7)(W + 12) which means W = 7, -12.

However, Width obviously cannot be a negative number. Thus, the width of the rectangle is 7 meters.

Step 4 Check your work:

if the width is 7 then the length must be 7+5 =12 and the area must be 12*7 = 84. Thus the width of the pen is 7 meters.