PYTHAGORAS THEOREM
What is the Pythagoras Theorem?
The Pythagoras Theorem, also referred to as the Pythagorean Theorem, was
introduced by the Greek Mathematician and Philosopher,
Pythagoras of Samos
.
It deals with a specific type of triangles called a
right-angled triangle
(one of the angles is 90o). It describes the relationship between the three sides
of the right-angled triangle.
It states that in a right-angled triangle, the square of the longest side (H2) is equal
to the sum of the squares of the other two sides of the triangle (B2 + P2).
H2 = B2 + P2
Questions on Pythagoras Theorem:
1. Find the longest side of a right-angled triangle if two of its sides are 3 cm and 4 cm.
Soln: Let H be the longest side of the given right-angled triangle.
Let the other two sides be B = 3 cm and P = 4 cm.
Using Pythagoras Theorem, we have
H2 = B2 + P2
Or, H2 = 32 + 42
Or, H2 = 9 + 16
Or, H2 = 25
Or, H = √25
Or, H = √52
Or, H = 5 cm
Hence, the longest side of the given right-angled triangle is 5 cm.
2. Find the longest side of a right-angled triangle if two of its sides are 7 cm and 24 cm.
3. Find the longest side of a right-angled triangle if two of its sides are 33 cm and 56 cm.
[NOTE: Using the Pythagoras Theorem, it is always possible to find a missing side of a right-angled
triangle, provided that two of its sides are given. It must be identified which side is the longest side,
H, to be able to use Pythagoras Theorem to find the missing side.]
Perpendicular (P)
Base (B)
Hint: To find the squared root of 25,
we use prime factorisation method
to find the factors of 25, which is 5.
Prime Factorisation: 25 = 5 x 5 = 52
