Page 21 - 新思维数学活动用书9 样章

2 Expressions and formulae

e When a is a positive integer, will the perimeter of the rectangle always be positive? Explain
your answer.
f Work out the perimeter of the rectangle when
i a = −1 ii a = −2 iii a = −3.
g Are your answers to part f valid measurements for the perimeter? Explain your answer.
Are there any negative values of a for which the perimeter is a valid measurement?

14 a Write an expression for the perimeter of this rectangle.

2x – 5x
2
4x + 3x
2
b Show that the expression in part a can be simplified to 4x(3x − 1).
c Read what Arun says.

When x = 3 and
when x = −3, you get
the same perimeter.

Is Arun correct? Explain your answer. Show your working.

15 a A cube has a volume of 27 cm . Show that the total length of all the edges of the cube is
3
36 cm.
b A cube has a volume of 64 cm . Work out the total length of all the edges of the cube.
3
c A cube has a volume of x cm . Write an expression for the total length of all the edges of the
3
cube. Use your working for parts a and b to help you.

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