Question

The triangle ABC has a line AP and the Perpendicular AO.

If Ratio of BO and OC is 10 : 7 and Area of Triangle AOC = $42c{m}^2$ , Find the Area of full triangle ABC

• A. $112c{m}^2$
• B. $100c{m}^2$
• C. $102c{m}^2$
• D. $108c{m}^2$

Answer 1

The correct option is C

$102c{m}^2$

Area of Triangle AOC : Area of triangle AOB = OC : BO = 7 : 10

10(Area of Triangle AOC) = 7(Area of triangle AOB)

$\Rightarrow$ 7(Area of triangle AOB) = 10 $\times$ 42 = $420c{m}^2$

$\Rightarrow$ $60c{m}^2$ = $\frac{420}{7}$ = $60c{m}^2$

$\therefore$ Area of triangle ABC = Area of Triangle AOC + Area of triangle AOB = 42 + 60 = $102c{m}^2$