Question

In the adjoining figure, BM = 2CM. If ar (ΔАBC) = 30 cm², then ar (ΔABM) is:

Options

• 20 cm²

• 15 cm²

• 10 cm²

• 5 cm²

Answer 1

20 cm² 

Explanation:

Triangles ABM and ABC share the same altitude from A.

So, their areas are proportional to their bases on BC. 

Since BM : CM = 2 : 1.

BC = BM + CM = 3 parts.

So, `"area"(ABM) = (BM)/(BC) xx "area" (ABC)`

= `(2/3) xx 30`

= 20 cm²