## Uses of Pythagoras’ Theorem

You may have heard about Pythagoras's theorem (or the Pythagorean Theorem) in your math class, but what you may fail to realize is that Pythagoras's theorem is used often in real life situations. Gain a better understanding of the concept with these real-world examples.

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

## Real Life Applications

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

**1) Road Trip:** Let’s say two friends are meeting at a playground. Mary is already at the park but her friend Bob needs to get there taking the shortest path possible. Bob has two way he can go – he can follow the roads getting to the park – first heading south 3 miles, then heading west four miles. The total distance covered following the roads will be 7 miles. The other way he can get there is by cutting through some open fields and walk directly to the park. If we apply Pythagoras's theorem to calculate the distance you will get:

(3)^{2 }+ (4)^{2} =

9 + 16 = C^{2}

√25 = C

5 Miles. = C

Walking through the field will be 2 miles shorter than walking along the roads. .

**2) Painting on a Wall:** Painters use ladders to paint on high buildings and often use the help of Pythagoras' theorem to complete their work. The painter needs to determine how tall a ladder needs to be in order to safely place the base away from the wall so it won't tip over. In this case the ladder itself will be the hypotenuse. Take for example a painter who has to paint a wall which is about 3 m high. The painter has to put the base of the ladder 2 m away from the wall to ensure it won't tip. What will be the length of the ladder required by the painter to complete his work? You can calculate it using Pythagoras' theorem:

(5)^{2 }+ (2)^{2} =

25 + 4 = C^{2}

√100 = C

5.3 m. = C

Thus, the painter will need a ladder about 5 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 Pythagoras' theorem. It is calculated this way:

(18)^{2 }+ (b)^{2} = (30)^{2}

324 + b^{2} = 900

B^{2} = 900 – 324

b= √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 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.