Question

Using a scale of $1cm$ to $1$ unit for both the axes, draw the graphs of the following equations:

$6y=5x+10$, $y=5x-15$.
From the graph find the area of the triangle between the lines and the $x$-axis.

• A. $14.5$ sq.unit
• B. $13.5$ sq.unit
• C. $11.5$ sq.unit
• D. $12.5$ sq.unit

Answer 1

The correct option is D $12.5$ sq.unit

Given : $6y=5x+10$

$⟹y=\frac{5x+10}{6}$

Let, $x=4$, then $y=\frac{5\left(4\right)+10}{6}=4$

Similarly, when $x=-2,y=0$

Now, $y=5x-15$,

Let, $x=3$, then, $y=5\left(3\right)-15=0$

Similarly, when $x=2,y=-5$

Triangle formed is $A(-2,0),B(4,5),C(3,0)$

$\therefore$ Area of the triangle formed is $=\frac{1}{2}\times b\times h$

$=\frac{1}{2}\times 5\times 5=12.5squnits.$