The line \(3x+4y=24\) forms a triangle with the two coordinate axes. What is the area of this triangle?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 24 square units
The line meets the x-axis where \(y=0\) and the y-axis where \(x=0\). With the origin, these two points form a right triangle whose legs are the two intercepts.
x-intercept: \(3x=24\), so \(x=8\); the line meets the x-axis at \((8,\,0)\)
y-intercept: \(4y=24\), so \(y=6\); the line meets the y-axis at \((0,\,6)\)
Area \(\displaystyle =\frac{1}{2}\times8\times6=24\) square units
