Year 9 Interactive Maths - Second Edition

Problem Solving

Example 15

A ladder 5.8 m long stands on level ground and its top just reaches the top of a wall 4.1 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 of the foot of the ladder from the wall is 4.1 m.

Example 16

A square schoolyard has sides 47 m long.  Find:

a.  the distance from one corner to the opposite corner correct to the nearest metre.
b.  how much further you would walk if you had to follow a path along two sides instead of 'cutting' across.

     So, the length of the diagonal is 66 m (to the nearest metre).

b.  The path along the two sides covers a distance of 94 m, and this is 94 – 66 = 28 metres longer than going straight across.

Navigation Problem

Example 17

A ship sails 42 km due east and then 25 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,

So, the ship is 48.88 km from the starting point.

Example 18

The length of the diagonal of a rectangular paddock is 61 m and the length of one side is 60 m.  Find:

Solution:

So, the width of the paddock is 11 m.

So, the length of the fence required to enclose the paddock is 142 m.

Example 19

Solution:

Study Another Topic in Chapter 3: Pythagoras' Theorem

[ Squares ] [ Square Roots ] [ Cubes ] [ Cube Roots ] [ Order of Operations ] [ Pythagoras' Theorem ] [ Finding a Short Side ] [ Pythagorean Triples ] [ Problem Solving ] [ Using a Construction Line ] [ Pythagoras' Theorem in Three Dimensions ] [ Problem Solving Unit ] [ Projects ] [ Symbols ] [ Index ]