Higher June 2019 Paper 3 Q14
14 The diagram shows a rectangle, \(ABDE\), and two congruent triangles, \(AFE\) and \(BCD\).
area of rectangle \(ABDE\) = area of triangle \(AFE\) + area of triangle \(BCD\)
\(AB : AE = 1 : 3\)
Work out the length of \(AE\). (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| 36 | P1 | for process to find an expression for the area of triangle eg \(\tfrac{1}{2} \times 24 \times AE \times \sin 30\ (= 6AE)\) |
| P1 | (dep P1) for process to link the area of rectangle with the area of the triangle eg \(2 \times \tfrac{1}{2} \times 24 \times AE \times \sin 30\ (= 12AE)\) or for \(AB = 12\) | |
| P1 | (indep) for use of given ratio eg \(AE = 3AB\) oe, eg area of rectangle = \(AE \times AB = 3x \times x\) | |
| A1 | cao |
Additional guidance
Accept any correct expression, eg \(\tfrac{1}{2} \times 24 \times y \times \sin 30\)
May be shown on the diagram by labelling \(AE\) and \(AB\) with, for example, \(3x\), \(x\) or \(x\), \(\tfrac{1}{3}x\) or \(\tfrac{3}{4}x\), \(\tfrac{1}{4}x\)
Do not accept 3, 1 or 1, \(\tfrac{1}{3}\) or \(\tfrac{3}{4}\), \(\tfrac{1}{4}\) for this mark.