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9.2 Constructing algebraic expressions

2 Write an expression for i the perimeter ii the area of each rectangle.
Write each expression in its simplest form.
a b c d 2y
x 4x x

y 3y x 2y

3 This is part of Mia’s homework.

Question Write an expression for the perimeter and area of this
rectangle. x + 5
Write each answer in its simplest form.
2x
Answer Perimeter = x + 5 + 2x + x + 5 + 2x Area = 2x(x + 5)

= 6x + 10 = 2x + 10x
2

To simplify the expression for the area of the rectangle, Mia has expanded the brackets.
Write an expression for the perimeter and area of each of these rectangles.
Write each answer in its simplest form.

y – 6 p + 3
x + 2 n + 4
a 3 b 4 c n d 4p

4 Alicia and Razi have rods of four different colours. x + 1 x + 2
The blue rods have a length of x + 1.
The red rods have a length of x + 2. 2x + 1 3x
The green rods have a length of 2x + 1.
The yellow rods have a length of 3x. x.
Alicia shows Razi that the total 3 red + 5 yellow 6 green + 2 yellow
length of 3 red rods and 5 yellow = 3(x + 2) + 5(3x) = 6(2x + 1) + 2(3x)
rods is the same as 6 green rods = 3x + 6 + 15x = 12x + 6 + 6x
and 2 yellow rods, like this. = 18x + 6 = 18x + 6
a Show that: i the total
length of 2
red rods and 2 yellow rods is the same as 4 green rods
ii the total length of 3 red rods and 3 yellow rods is the same as 6 green rods
iii the total length of 4 red rods and 4 yellow rods is the same as 8 green rods.
b What do your answers to part a tell you about the connection between the number of red and
yellow rods and green rods?
c Show that: i the total length of 3 red rods and 1 yellow rod is the same as 6 blue rods
ii the total length of 6 red rods and 2 yellow rods is the same as 12 blue rods
iii the total length of 9 red rods and 3 yellow rods is the same as 18 blue rods.
d What do your answers to part c tell you about the connection between the number of red and
yellow rods and blue rods?

9 Expressions and formulae 87