Question

The triangle ABC is given below :

The areas of AOB and AOC are in the ratio 14 : 20

If the area of the smaller triangle is $24c{m}^2$ less than the area of larger triangle, find the total area of the triangle ABC.

• A. $156c{m}^2$
• B. $136c{m}^2$
• C. $162c{m}^2$
• D. $142c{m}^2$

Answer 1

The correct option is B

$136c{m}^2$

Let area of $\Delta AOB$ be 14x and that of $\Delta AOC$ be 20x

According to the question : 14x = 20x - 24

$\Rightarrow$ 20x - 14x = 24

$\Rightarrow$ 6x = 24

$\Rightarrow$ x = $\frac{24}{6}$ = 4

$\therefore$ Area of $\Delta ABC$ = Area of $\Delta AOB$ + Area of $\Delta AOC$ = 14x + 20x = 34x = 34$\times$4 = $136c{m}^2$