In ΔABC, a line through A cuts the side BC at D such that BD : DC = 4 : 5. If the area of ΔABD = 60 cm², then the area of ΔADC is:

Height will be same for both triangles

In triangles ADB, if base = 4x and area = 60 cm²
Area of ΔADB = 60 cm²
$$\frac{1}{2}$$ × base × height = 60
⇒ $$\frac{1}{2}$$ × 4x × height = 60
⇒ height = $$\frac{{60}}{{2x}}$$
⇒ height = $$\frac{{30}}{x}$$ cm
⇒ Therefore using height Area of ΔADC will be
= $$\frac{1}{2}$$ × base × height
= $$\frac{1}{2}$$ × 5x × $$\frac{{30}}{x}$$
= 75 cm²