Question

In the given figure, ABC is a triangular plot, OE = OF = OG = 2 cm. If the area of the plot is 40 cm${}^2$, then the semi-perimeter of the ΔABC is

• A. 40 cm
• B. 20 cm
• C. 50 cm
• D. 80 cm

Answer 1

The correct option is B 20 cm

Given: OE = OF = OG = 2 cm
Area of the triangular plot ABC = 40 cm${}^2$
$\Rightarrow$ Area of $\Delta AOB$ + Area of $\Delta BOC$ + Area of $\Delta AOC$= 40 cm${}^2$
$\Rightarrow \frac{1}{2}\times AB\times OE+\frac{1}{2}\times BC\times OF+\frac{1}{2}\times AC\times OG=40$
$\Rightarrow \frac{1}{2}\times 2\times (AB+BC+AC)=40$ ($\therefore OE=OF=OG=2cm$)
$\Rightarrow AB+BC+AC=40cm$
$\therefore$ Semi-perimeter of $\Delta ABC=\frac{1}{2}\times (AB+BC+AC)$
$=\frac{1}{2}\times 40$
= 20 cm
Hence, the correct answer is option (b).