Question

The area of the triangle formed by the lines $7x+3y=35,x=5,2y-3=0$ is

• A. $\frac{27}{28}$
• B. $\frac{17}{28}$
• C. $\frac{13}{25}$
• D. $\frac{27}{56}$

Answer 1

Answer: (D)

$\frac{27}{56}$

$7x+3y=35$

$x=5$ and $y=\frac{3}{2}$

So, $7x+3y=35$ and $y=\frac{3}{2}$

$\Rightarrow 7x+\frac{9}{2}=35$

$7x=\frac{61}{2}$

$x=\frac{61}{14},y=\frac{3}{2}$

$\therefore$ area of $△ABC=\frac{1}{2}\times AC\times AB$

$=\frac{1}{2}\times (5-\frac{61}{14})\left(\frac{3}{2}\right)$

$=\frac{1}{2}\times \frac{9}{14}\times \frac{3}{2}$

$=\frac{27}{56}$