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?

### Development:

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.

### Solution:

My grandfather has to buy $$19,7$$ meters of ribbon.