A rectangle has a perimeter of 46 cm and a diagonal of 17 cm. What is its area?

Let the sides be $l$ and $w$. The perimeter gives $l+w=23$ and the diagonal gives $l^2+w^2=17^2=289$. Squaring the first, $(l+w{)}^2=529=l^2+w^2+2lw=289+2lw$, so $2lw=240$ and the area $lw=120{\text{cm}}^2$. (The sides work out to 8 cm and 15 cm, and $8^2+15^2=289$.) Stopping at $2lw$ gives $240{\text{cm}}^2$.