Mathematical Methods — Question 18

QCAA 2020, Paper 2 · 4 marks

Q18 · 2020 · Technology-activeComplex familiar4 marks

QUESTION 18 (4 marks)

The diagram shows the quadrilateral

ABCD

. Determine the perimeter of the quadrilateral.

WORKED SOLUTION

4 marks

ANSWER

28.5865\;\mathrm{cm}

Worked solution

Construct diagonal

BD

. By the cosine rule,

BD^2=4.1^2+7.6^2-2(4.1)(7.6)\cos117^\circ,

BD=10.142

cm. Then

10.142^2=5.4^2+DC^2-2(5.4)(DC)\cos62^\circ.

Solving gives

DC=11.4865

cm. Therefore the perimeter is

11.4865+5.4+4.1+7.6=28.5865

cm.

correctly determines

BD

[1 mark]

establishes equation in

DC

[1 mark]

determines

DC

[1 mark]

determines perimeter

[1 mark]

One QCAA sample method typeset for web; criterion wording is adapted from the official marking guide.

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