Leon's L Shaped Birthday Cake

Question

Leon's father has baked him an L-Shaped cake for his birthday, with the dimensions as shown:

https://imgur.com/VFMYHnA

The height of the cake is 5 cm.

Leon's mother suggests that Leon slices the cake into three pieces with a single straight cut, so that the pieces are in the ratio 1 : 2 : 3. Can you find a way for Leon to do this? Show working.

Answer 1

Label the diagram with the lower left corner at (0, 0). Label all corner points.

The single slice must cut the 40 cm side and the 30 cm side while touching the crux of the L.

Label the cut through the 30 cm side at (x, 0) and the 40 cm side (0, y).

You now have two trapezoids and a triangle.

Determine expressions for the area of each.

Set them in the ratio of 1 : 2 : 3 and solve the system for x and y.