Question

Figure shows the graph of $y=f\left(x\right)$ defined by $f\left(x\right)=\frac{180}{x+3}$ for $x\ge 0$, and $f\left(x\right)=60$ for $x<0$. Find the sum of the areas of the three shaded rectangles.

• A. $111$
• B. $135$
• C. $141$
• D. $180$
• E. $195$

Answer 1

Answer: (C)

$141$

Given, $f\left(x\right)=\frac{180}{x+3}$

$\therefore f\left(6\right)=\frac{180}{9}=20$ , $f\left(9\right)=\frac{180}{12}=15$ , $f\left(12\right)=\frac{180}{15}=12$
So the area of first shaded region is $f\left(6\right)\times (6-3)=20\times 3=60$
The area of second shaded region is $f\left(9\right)\times (9-6)=15\times 3=45$
The area of third ahaded region is $f\left(12\right)\times (12-9)=12\times 3=36$
Sum of areas of shaded regions is $60+45+36=141$.