A rectangular plot covers 60 square metres and its diagonal measures 13 m. What is the length of fencing, in metres, needed to go once round the plot?

Let the sides be $l$ and $b$. The diagonal gives $l^2+b^2=169$ and the area gives lb = 60. Then $(l+b{)}^2=l^2+b^2+2\text{lb}=169+120=289$, so $l+b=17$ and the fencing = $2(l+b)=34$ m. (The sides are 12 m and 5 m.) The trap 17 quotes the half-perimeter and forgets to double it; 14 comes from $(l-b{)}^2=169-120=49$, subtracting 2lb where it should be added, which gives the DIFFERENCE of the sides, not their sum; 26 doubles the diagonal, treating it as though it were half the boundary.