A triangle is formed by the line 3x + 4y = 12, the x-axis and y-axis. The circumradius is

2.5

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Solution

The correct option is A
2.5

When we draw the given line on graph paper

The figure formed by line 3x+4y=12, the x-axis and y-axis, is a right-angled triangle.

Substitute y = 0 to obtain the x-intercept
x-intercept = 4

Substitute x = 0 to obtain the y-intercept
y-intercept = 3

As we know that, circumradius of a right angled triangle is half of the length of its hypotenuse.

$H y p o t e n u s e^{2} = (l e n g t h o f x - i n t e r c e p t^{2}) + (l e n g t h o f y - i n t e r c e p t^{2})$

Hypotenuse = $\sqrt{(4^{2} + 3^{2})}$

= 5

Circumradius = $\frac{1}{2} \times h y p o t e n u s e$ = $\frac{5}{2}$

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