Question

3. From the coordinates of the triangle formed by the line 4x - 5y-20 =0, 3x +5y -15 = 0 and
Y-axis, the area of triangle is
(a) 25 sq units (6) 2 sq units
(c) 35 sq units (d) 53 sq units
sq units​

Answer 1

35/2

Given line equations 4x - 5y-20 =0, 3x +5y -15 = 0 and x=0(y-axis)

There are several ways to do it and I recommend to do this:

1) First take down the 3 equations which are given and name them as eq 1,2&3

2)Solve 1&2 then 2&3 and finally 3&1.

3)You'll get three points name them as a(x1,y1),b(x2,y2) and c(x3,y3)

4)By using formula area=(1/2)×[x1(y2-y3)+x2(y3-y1)+x3(y1-y2)] calculate the area

5)Thus your area is obtained.

Answer 2

Area of the triangle is $\frac{35}{2}$ sq. units.

Step-by-step explanation:

The three equations forming the triangle are

4x - 5y - 20 = 0 .......... (1)

3x + 5y - 15 = 0 ........... (2)

And, x = 0 (i.e. y-axis) .......... (3)

Now, solving the equations (1) and (2) we get

4x + 3x - 20 - 15 = 0

⇒ 7x - 35 = 0

⇒ x = 5

Then, from equation (1) we get,

4(5) - 5y - 20 = 0

⇒ y = 0

So, equation (1) and (2) intersect at (5,0) point.

Now, solving equations (1) and (3) we get the point of intersection is (0,- 4).

Again, solving equations (2) and (3) we get the point of intersection is (0,3).

Therefore, the vertices of the triangle are (5,0), (0,-4), and (0,3).

Hence, the area of the triangle will be

= $\frac{1}{2}|5(- 4 - 3) + 0 + 0|$

= $\frac{35}{2}$ sq. units. (Answer)