Question

In the given figure, the equation of the line L1 is and area of ΔOAB is 15 sq. units. Then, the value of a is equal to

Answer 1

The equation of line is given as:

$\dfrac{x}{5} + \dfrac{y}{a} = 1$

In general, the intercept form of equation of a straight line is given by:

$\dfrac{x}{A} + \dfrac{y}{B} = 1$

Where A is the x intercept of line (i.e. value of x when y is 0)and

B is the y intercept of line (i.e. value of y when x is 0)

Comparing the given equation of straight line with standard equation of line:

x intercept  of line L1, A = 5

y intercept  of line L1, B = a

x and y intercepts form a right angled triangle with origin having the right angle.

This right angled triangle is ΔOAB and area is  15 sq units.

Area of a triangle is given as:

$A = \dfrac{1}{2} \times Base \times Height$

Here, Base is the x intercept = 5

Height is the x intercept = a

Putting values in the Area formula:

$15=\dfrac{1}{2} \times 5 \times a\\\Rightarrow a = \dfrac{30}{5} = 6$

So, a = 6 units.