Pythagorean Theorem Word Problems

In this lesson, we will be looking at several word problems that use the Pythagorean theorem.

Example:

Shane marched 3 m east and 6 m north. How far is he from his starting point?

Solution:

First, sketch the scenario. The path taken by Shane forms a right-angled triangle. The distance from the starting point forms the hypotenuse.

x = = 6.71 m

Example:

The rectangle PQRS represents the floor of a room.

Ivan stands at point A. Calculate the distance of Ivan from

a) the corner R of the room

b) the corner S of the room

Solution:

a) AR = = 4.47 m

Ivan is 4.47 m from the corner R of the room

b) AS = = 10.77 m

Ivan is 10.77m from the corner S of the room

Example:

In the following diagram of a circle, O is the centre and the radius is 12 cm. AB and EF are straight lines.

Find the length of EF if the length of OP is 6 cm.

Solution:

OE is the radius of the circle, which is 12 cm

OP 2 + PE 2 = OE 2

6 2 + PE 2 = 12 2

PE =

EF = 2 × PE = 20.78 cm

The following video gives another example of Pythagorean theorem word problem.

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