Pythagoras theorem a nightmare during grade school

As an up and coming student of science in 9th grade, I had some difficulty in understanding some theorems in mathematics. One I could remember very well was Pythagoras theorem.

I always question the correctness of the theorem anytime my tutor mentions or applies the theorem in class.

This theorem states that having a triangle as the one below

The square of the distance d plus the square of the distance h is equal to the square of the distance g.

This can be written mathematically as

d2 + h2 = g2

I was having a hard time grasping this theorem. This is because just having a critical look at this triangle, adding the distance of d and h will definitely be longer than the distance g let alone squaring them. I always perform poorly in mathematical exams when I am to apply this theorem in solving a particular question.

I strongly believe most scientist have one way or the other suffer this ordeal before?

I gained much understanding of this theorem during my first year in high school. This came into play when talking about real life applications of Pythagoras theorem.

Some basic real-life applications of mathematics are as listed below.

Imagine 3 friends going on a trip to Sydney by Tran. They decided to meet at a train station at exactly 9:00am in the morning on Thursday. On the said day, John and Frank were already at the station but their friend Cynthia needs to arrive at the station as soon as possible. This is because the train has barely less than 40 minutes to move. Cynthia has 2 ways in which he can arrive at the station. First, she has to move north 3 miles then after head 4 miles east. The other way she can get to the station is by cutting via some open fields and walk directly to the station. John and Frank can use Pythagoras theorem to calculate the shortest distance to the station in order that Cynthia wouldn’t miss the train.

This can be calculated in this way applying Pythagoras

We said that Cynthia can ply north and then east which happens to be the first road. John and Frank also know the distance that Cynthia will cover plying that road.

From Pythagoras we know that d2 + h2 = g2 . If we assume the distance to the north is represented by d and that of east is represented by h. Then we can find the distance when Cynthia cuts via the open field which can be represented by g.


    9 + 16 = (g)2

  25 = (g)2

  √25 = √g2

g=5 miles

This shows that it will be in the best interest of Cynthia to cut via the fields. This is because that is the shortest distance with which she can get to the train station on time.