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Pythagorean theorem
My grandfather loves the sea, and with the money he had been saving for many years he decided to buy a sailboat. He has found a nice sailboat for sale, but needs to re-do the sails. My grandfather has accepted the offer and seizes the opportunity to decorate them as he likes.
The front sail he wants to decorate with a special color ribbon that goes around the entire perimeter of the sail, i.e. color the edge. How many meters of ribbon does he need to buy?
The sail has the shape of a right triangle, and we know the length of the legs, $8$ and $3.10$ meters respectively. Now, we need to know the length of the hypotenuse.
Therefore we use the Pythagorean theorem, which tells us that if $h$ is the length of the hypotenuse and $c_1$ and $c_2$ are the lengths of the legs we have to isolate the hypotenuse: $h^2=c_1^2+c_2^2$.
$$h=\sqrt{c_1^2+c_2^2}=\sqrt{8^2 + 3,10^2}=\sqrt{64 + 9,61} = \sqrt{73,61}=8,6$$
Therefore the hypotenuse measures $8.6$ meters.
In total, he will need to purchase $8,6+8+3,1=19,7$ meters.
My grandfather has to buy $19,7$ meters of ribbon.