Problems from 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.

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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?

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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.

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