The figure ABCD is a square with side length a + b, and
it consists of the four congruent right-angled triangles and a square, EFGH,
with side length c.
This proof was devised by the Indian mathematician, Bhaskara, in 1150
Applications of Pythagoras' Theorem
To solve a word problem, read the problem and draw a diagram. Then
write the given information on the diagram and identify any right-angled
triangle(s). Use Pythagoras' Theorem to form an equation and solve
the equation thus obtained. Translate the solution into a worded
A ship sails 80 km due east and then 18 km due north. How far is the
ship from its starting position when it completes this voyage?
Let the distance of the ship from its starting point be x km. We
can draw a diagram of the ship's voyage on a set of axes, with the
horizontal axis representing east and the vertical axis representing
north. The ship is at the point P and it started at the origin.
There is a right angle at A.
By Pythagoras' Theorem from triangle OAP,
A ladder 7.25 m long stands on level ground so that the top end of the
ladder just reaches the top of a wall 5 m high. How far is the foot of the
ladder from the wall?
Let the distance from the foot of the ladder to the base of the wall be x m.
By Pythagoras' Theorem and the diagram,
So, the distance from the foot of the ladder to the wall is 5.25 m.
Using a Construction Line
Sometimes we need to draw a construction line (shown as a broken line)
in the diagram to form a right-angled triangle.
Use the information given in the following diagram to find the value of x.
Join BD by a broken line to form the right-angled triangles ABD and BCD. Let BD = y cm.