How long is DC?

A normal-level "Length" problem."Same height, so area ratio = base ratio" works in both directions — lengths to areas, and areas back to lengths.

GivenTriangle ABC has area 60 cm², triangle ABD has area 24 cm². BC = 15 cm

Hints

First, the area of the remaining triangle ADC — just subtract: 60 − 24 = 36 cm².
Triangles ABD and ADC both have apex A, and their bases BD and DC lie on the same line — so they share the same height.
Same height means area ratio = base ratio. Usually we go from sides to areas; here we go backwards, from areas to sides: 24 : 36 = 2 : 3, which is BD : DC.
BC is split into 5 parts, and DC is 3 of them.
BC is 15 cm, so the answer is 15 ÷ 5 × 3.

Answer 9cm