Math Problem : J.2 Overlapped two triangles

△DBE and △ABC are overlapped as shown in the figure below.

AB : DB = 7 : 3 and BC : BE = 8 : 5.

The area of △DBE is 15 cm².

Find the area of △ABC.

Answer

56 cm²

Solution

The area ratio of △ABC and △DBE is set to (7 × 8) : (3 × 5) = 56 : 15.

Since △DBE is 15 cm², △ABC is 15 × (56/15) = 56 cm².