Page 31 - 新思维数学学生用书9 样章

2 Expressions and formulae

7 The diagram shows a triangle.

The lengths of the sides of the triangle are written as expressions.
a Work out the lengths of the sides of the triangle when w = 2 (3w) 2 2v(3v – 2w)
and v = 3.
b Use your answers to part a to work out the perimeter of the 5w(w + v)

triangle when w = 2 and v = 3.
c Write an expression for the perimeter of the triangle.
Show that the expression can be simplified to 14w + vw + 6v .
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d Substitute w = 2 and v = 3 into the expression for the perimeter from part c.
Check that your answers to parts b and d are the same.

Think like a mathematician

8 Work with a partner to answer this question.

The diagram shows a quadrilateral.
The lengths of the sides of the quadrilateral are written as expressions.

3a – 7b
2
8b – 3a
a + 6b
2
4(a + 3b)
a Work out the lengths of the sides of the quadrilateral
when a = −5 and b = 2.
b Use your answers to part a to work out the perimeter of the quadrilateral

when a = −5 and b = 2.
c Write an expression for the perimeter of the quadrilateral.
Show that the expression can be simplified to a + 4a + 19b.
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d Use the expression in part c to work out the perimeter of the quadrilateral
when a = −5 and b = 2.
Are your answers to parts b and d the same? If not, check your working.
e Work out the perimeter of the quadrilateral when a = 4 and b = −3.
f Is your answer to part e a valid measurement for the perimeter?

Explain your answer.
Discuss your answer with other learners in your class.

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