Question

Find the area of the triangle formed by the line $4x+5y+7=0$ with the coordinate axes.

• A. $\frac{51}{40}$
• B. $\frac{49}{40}$
• C. $\frac{39}{40}$
• D. $\frac{31}{40}$

Answer 1

The correct option is B $\frac{49}{40}$

Let the given line $4x+5y+7=0$ cuts the coordinate axes at $A(\alpha ,0)$ and $B(0,\beta )$

The traiangle formed by this line and coordinate axes will be a right angled triangle, with base $\alpha$ and height $\beta$.

Area of triangle $A=\frac{1}{2}\times |\alpha |\times |\beta |$

Now putting $y=0$ and $x=0$ to find $\alpha$ and $\beta$ respectively.

We get, $\Rightarrow \alpha =-\frac{7}{4}$

$\Rightarrow \beta =-\frac{7}{5}$

Hence $A=\frac{1}{2}\times \frac{7}{4}\times \frac{7}{5}$

Area if triangle is $\Rightarrow A=\frac{49}{40}$

Correct option is $B$.