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G S Rehill's Interactive Maths Software Series - "Building a Strong Foundation in Mathematics" from mathsteacher.com.au.

Order a 12-month Year 7 Interactive Maths software Homework Licence for only $19.95. Order a 12-month Year 8 Interactive Maths software Homework Licence for only $19.95. Order a 12-month Year 9 Interactive Maths software Homework Licence for only $19.95. Order a 12-month Year 10 Interactive Maths software Homework Licence for only $19.95.

Year 10 Interactive Maths - Second Edition


Problem Solving

We can use the Distributive Law and/or perfect squares to express the area of figures in terms of a variable, x.

Example 12

The length of the side of a square paddock is x m. If one side of the paddock is lengthened by 8 m and the adjacent side is shortened by 3 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 m squared, (c) the area of the square paddock
Solution:
(a) l = (x + 8) m, w = (x - 3) m.

Thus A = lw = x squared + 5x - 24.

 a square of side-length x m and a rectangle of length (x + 8) m and width (x - 3) m
(b) If A = 80, then x = 8.

(c) Area of the square paddock = 64 m squared.

 

Example 13

A square picture is fixed in the middle of a square picture 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 cm squared, of the frame in terms of x.

Solution:

(a) l = 17 + 2x

(b) A = 289 + 68x + 4(x squared)

  

 

The square picture and square picture frame.

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