Year 9 Interactive Maths - Second Edition

Problem Solving

Example 6

The length of the side of a square paddock is x m.  If one side of the paddock is lengthened by 7 m and the adjacent side is shortened by 4 m so as to make the paddock rectangular, find:

a.  an expression for the area, A, of the rectangular paddock in terms of x
b.  the value of x, when the area of the rectangular paddock is 80 m²
c.  the area of the square paddock using the answer to b.

Solution:

Example 7

A square picture is fixed in the middle of a square frame as shown in the diagram.  If the width of the border is x cm, express:

a.  the length, l cm, of the frame in terms of x.
b.  the area, A cm², of the frame in terms of x.

Solution:

Example 8

A cyclist takes (x + 2) hours to travel a distance of 80 kilometres when cycling at x kilometres per hour.  Find:

a.  the value of x
b.  the time taken to complete the journey

Solution:

Example 9

A rectangular flower-bed 8 m by 6 m is surrounded by a concrete path, as shown in the diagram.  If the area of the path is 32 m², find:

a.  the value of x
b.  the width of the path

Solution:

a.  From the diagram, we see that the outer rectangle is (8 + 2x) metres long and (6 + 2x) metres wide.