Pythagoras was a Greek philosopher and mathematician. Whether you know it or not, the Pythagoras theorem, named after him, is used by almost everybody in real life experiences.

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### Uses of Pythagoras Theorem

You may have heard about the Pythagoras theorem in your math class. But what you may fail to realize is that the Pythagoras theorem is used often in real life situations. Gain a better understanding of the concept with these real-world examples.

According to the Pythagoras theorem the sum of the squares of two sides of a right triangle is equal to the square of the hypotenuse. E.g. Let one side of the right triangle is a, the other side is b and hypotenuse is given by c. According to the Pythagoras theorem

a

^{2}+ b^{2}= c^{2}This is taught in every classroom throughout the world, but what isn't taught is how it can be applied outside of the classroom.

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### Real Life Applications

Some real life applications to introduce the concept of the Pythagoras theorem to your middle school students are given below:

**1) Road Trip:**Let’s say two friends are meeting at a playground. One friend is located on the south-west corner of playground and other is located on the north-east corner of the playground. There are two ways to go let us see how you can take the help of Pythagoras theorem to calculate the shortest distance between the meeting points of two friends. If you follow a road 3 miles east and then 4 miles north. Your total distance covered will be 3+4 = (7) miles but if you apply the Pythagoras theorem to calculate the distance you will get:(3)

^{2 }+ (4)^{2}=9 + 16 = C

^{2}√25 = C

5 Miles. = C

So this will save them 2 miles distance.

**2) Painting on a Wall:**Painters use ladders to paint on high buildings and often use the help of the Pythagoras theorem to complete their work. Take for example a painter who has to paint a wall which is about 8 m high. The painter has to put the ladder 6 m away to avoid a rack in between. What will be the length of the ladder required by the painter to complete his work? You can calculate it using the Pythagoras theorem:(8)

^{2 }+ (6)^{2}=64 + 36 = C

^{2}√100 = C

10 Mts. = C

Thus, the painter will need a ladder 10 meters high.

**3) Buying a Suitcase:**Mr. Harry wants to purchase a suitcase. The shopkeeper tells Mr. Harry that he has a 30 inch of suitcase available at present and the height of the suitcase is 18 inches. Calculate the actual length of the suitcase for Mr. Harry using the Pythagoras theorem. It is calculated this way:(18)

^{2 }+ (b)^{2}= (30)^{2}324 + b

^{2}= 900B

^{2}= 900 – 324b= √576

= 24 inches

**4) What Size TV Should You Buy?**Mr. James saw an advertisement of a T.V.in the newspaper where it is mentioned that the T.V. is 16 inches high and 14 inches wide. Calculate the diagonal length of its screen for Mr. James. By using Pythagoras theorem it can be calculated as:(16)

^{2 }+ (14)^{2}=256 + 196 = C

^{2}√452 = C

21 inches approx. = C

**5) Finding the Right Sized Computer:**Mary wants to get a computer monitor for her desk which can hold a 22 inch monitor. She has found a monitor 16 inches wide and 10 inches high. Will the computer fit into Mary’s cabin? Use the Pythagoras theorem to find out:(16)

^{2 }+ (10)^{2}=256 + 100 = C

^{2}√356 = C

18 inches approx. = C

Practice Ideas

- Now write your own problem based on a potential real life situation.

### References

- Teaching experience.