In the diagram, BCD is a straight line and BC : CD = 3 : 5. Calculate the area of triangle ABC as a percentage of the area of the triangle ABD. Answer ...%

1. Find the ratio of the base $BC$ to the whole base $BD$.

Given $BC:CD=3:5$,

$BD=BC+CD=3+5=8\text{ parts}.$

So

$BC:BD=3:8.$

2. Convert the area ratio into a percentage.

Triangles $ABC$ and $ABD$ have the same height from $A$ to line $BD$, so

$\frac{\text{Area of }\triangle ABC}{\text{Area of }\triangle ABD}=\frac{BC}{BD}=\frac{3}{8}.$

As a percentage,

$\frac{3}{8}\times 100\%=37.5\%.$