Question

The area of triangle formed by the straight line 6x+4y=24 and coordinate

Answer 1

The straight line is :

6 x + 4 y = 24

In the slope - intercept form:

4 y = - 6 x + 24  / : 4   ( we can divide both sides of the equation by 4 )

y = - 3/2 x + 6

When y = 0 :

0 = - 3/2 x + 6

3/2 x = 6

x = 6 : 3/2 = 6 * 2/3 = 4

The triangle formed by the straight line and coordinate axis is the right triangle, with a = 4 and b = 6.

A = a * b / 2 = 4 * 6 / 2 = 24 / 2 = 12

Answer: The area of triangle is 12.

Answer 2

6x + 4y = 24 is a equation of straight line .
if we take y = 0, then 6x = 24 => x = 4
if we take x = 0, then 4y = 24 => y = 6

hence, graph cuts at (4,0) and (0, 6) respectively x and y axes. so, area enclosed by graph and co-ordinate axes is given by,
$\triangle=\frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]$

here, co-ordinates of triangle are (0,0), (4,0) and (0,6)
so, area of triangle = 1/2 [0 + 4(6 - 0) + 0]
= 1/2 × 24
= 12 sq unit