Maths Project.

~~Why is it named Pythagoras' Theorem?
Pythagoras' theorem is named after the Greek mathematician, Pythagoras for his discovery and proof on the Pythagoras' theorem.

~~What is Pythagoras' Theorem?
Pythagoras' Theorem is the sum of the areas of the two squares on the legs ( a and b)

~~What is hypotenuse?
The hypotenuse is the longest side of the triangle.

~~Equation
c² = a² + b²
c represents the length of the hypotenuse, and a and b represents the length of the other two sides.

~~Pythagorean Triplets
Pythagorean Triplets are numbers when the first and the second number are squared, the third number would always be the biggest number. 3, 4, 5 and 5, 12, 13 and 7, 24, 25.

~~Solving for c:
c = √ a² + b²

~~ Solving for a:
c² – b² = a²

~~Solving for b:
c² – a² = b²

Example 1:
If a = 3cm and b = 4cm, find the hypotenuse of the triangle.
We always start with “By Pythagoras' Theorem”

Solution:
By Pythagoras' Theorem,
c² = a² + b²
c² = (3cm)² + (4cm)²
c² = 25
c²=5²
c = 5
Therefore, the hypotenuse of the triangle is 5cm.

Example 2:
Question: A 5m long ladder is placed against a wall with its foot 1.8m from the wall. Find how far up the wall the ladder reaches.

Solution:
By Pythagoras' Theorem,
c² = a² + b²
5m = a² + 1.8m
a² = 5m² – 1.8m²
a² = 21.76
a² = 4.66²
Therefore, the ladder is 4.66m tall.

Testing.