Question

i) In the figure given below,, $XY\parallel BC$. Given that AX = 3 cm, BX = 1.5 cm and BC = 6 cm. Write down the value of XY

ii) If $\frac{AX}{XB}=\frac{4}{13}$ and AC = 20.4 cm, find AY. [3 MARKS]

Answer 1

Each part: 1.5 Marks

i) Since $XY\parallel BC$, so from $\Delta ABC$ and $\Delta AXY$
$\angle A=\angle A$ [Common]
$\angle AXY=\angle ABC$ [Corresponding angles]
$\therefore \Delta ABC\sim \Delta AXY$ [By A.A. axiom of similarity]
$\Rightarrow \frac{XY}{BC}=\frac{AX}{AB}$ [Ratio of corresponding sides ]
$\Rightarrow \frac{XY}{6}=\frac{3}{4.5}$
$\Rightarrow XY=\frac{3\times 6}{4.5}=4cm$

ii) Since $\Delta ABC\sim \Delta AXY$,
$\therefore \frac{AX}{XB}=\frac{AY}{YC}$ [Ratio of corresponding sides is equal]
$\Rightarrow \frac{AX}{XB}=\frac{AY}{AC-AY}$
$\Rightarrow \frac{4}{13}=\frac{AY}{20.4-AY}\Rightarrow 13AY=81.6-4AY$
$\Rightarrow 17AY=81.6\Rightarrow AY=\frac{81.6}{17}=4.8cm$
Hence, $AY=4.8cm$