Official papers

Official 2023 Paper 1 · Q8

Paper 1Geometry

A triangle XYZXYZ is called fun if it has the following properties:

angle YXZ=30∘XY=3 aYZ=a\begin{aligned}\text{angle }YXZ&=30^\circ\\XY&=\sqrt3\,a\\YZ&=a\end{aligned}

where aa is a constant.

For a given value of aa, there are two distinct fun triangles SS and TT, where the area of SS is greater than the area of TT.

Find the ratio

area of S:area of T.\text{area of }S:\text{area of }T.
A1:11:1
B2:12:1
C2:32:\sqrt3
D3:1\sqrt3:1
E3:13:1

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