A triangle is formed by X -axis, Y -axis and the line 3x + 4y = 60...

Given:

$3x + 4y = 60$

$⇒ \dfrac{x}{20} + \dfrac{y}{15} = 1$

If $x = 1, y = \dfrac{57}{4} = 14 . 25$

So, points are

\left(1, 1\right)\left(1, 2\right) - \left(1, 14\right) ⇒ 14$points.</p><p>If$x = 2, y = \dfrac{27}{2} = 13 . 5$</p><p>So, points are</p><p>\left(2, 2\right)\left(2, 4\right) \ldots \left(2, 12\right) ⇒ 6$ points.

If $x = 3, y = \dfrac{51}{4} = 12 . 75$

So, points are

\left(3, 3\right)\left(3, 6\right) - \left(3, 12\right) ⇒ 4$points.</p><p>If$x = 4, y = 12$</p><p>So, points are</p><p>\left(4, 4\right)\left(4, 8\right) ⇒ 2$ points.

If $x = 5, y = \dfrac{45}{4} = 11 . 25$

So, points are

\left(5, 5\right), \left(5, 10\right) ⇒ 2$points.</p><p>If$x = 6, y = \dfrac{21}{2} = 10 . 5$</p><p>So, point is</p><p>\left(6, 6\right) ⇒ 1$ point

If $x = 7, y = \dfrac{39}{4} = 9 . 75$

So, point is

\left(7, 7\right) ⇒ 1$point</p><p>If$x = 8, y = 9$</p><p>So, point is</p><p>\left(8, 8\right) ⇒ 1$ point

If $x = 9 ⇒ y = \dfrac{33}{4} = 8 . 25 ⇒$ no point

Total points inside the triangle

$= 31$ points