The area (in sq. units) of the triangle formed by the graphs of 8x + 3y = 24, 2x + 8 = y and the x-axis is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 28
Concept
Intercept form = x / a + y/ b = 1
Application
x / a + y/ b = 1
For 8x + 3y = 24, 2x + 8 = y to find the point of intersection put one equation in other
8x + 3(2x + 8) = 24
14x = 0
x = 0
y = 2×0 + 8 = 8
Height of the triangle = 8
For 8x + 3y = 24, 2x + 8 = y to find the X – intercepts put y = 0
8x + 3×0 = 24
x1 = 3
2x + 8 = 0
x2 = -4
Their difference is the base = 3 – (-4) = 7
Area of triangle = 1 /2 x b x h
= 1/2 x 7 x 8 = 28