The problem
We wanted to relax for a while and go and play football. When we got to the pitch we found Manel, the groundskeeper, looking worried. He wants to put a fence all round the pitch and has to cut it to size, but he cannot remember the exact measurements. On a piece of paper he has written that the perimeter of the pitch is $266$ m and the width is $44$ m; the length has been rubbed out. Let's help him.
Which concepts we will need
Essentially, equations.
1. A drawing of the pitch
Draw the pitch to get things clear.
See the solution
The pitch is a rectangle: opposite sides are equal. The two short sides are $44$ m; we do not know the two long ones.
A rectangle with two $44$ m sides and two sides of unknown length.
2. A letter for what we do not know
Give the unknown measurement a letter.
See the solution
We give the unknown length a letter. Since both long sides are equal, they are both $x$:
The sides of the pitch are $44$, $x$, $44$ and $x$.
3. The perimeter and the equation
Remember what the perimeter is, set up the equation and find the length of the pitch.
See the solution
The perimeter is the sum of all the sides:
Since the perimeter is $266$ m, we set up the equation and solve for $x$:
Check: $2 \cdot 44 + 2 \cdot 89 = 88 + 178 = 266$ m.
The pitch is $44$ m wide and $89$ m long. Manel must cut $266$ m of fencing: two $44$ m pieces and two $89$ m pieces.