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From the graph, we can conclude that the area of the triangle formed by the line $x + 3 y = 12$ and the coordinate axis is ____ sq units.

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Detailed Solution

From the graph, we can conclude that the area of the triangle formed by the line

x + 3 y = 12

and the coordinate axis is 24 sq units.
The point at which line x axis has its y coordinate is 0.
Substituting y = 0 in the equation,

⇒ x + 3 y = 12

⇒ x + 3 (0) = 12

⇒ x = 12

The point formed on x axis is (12,0).
The point at which line y axis has its x coordinate is 0.
Substituting x = 0 in the equation,

⇒ x + 3 y = 12

⇒ 0 + 3 y = 12

⇒ y = 4

The point formed on y axis is (0,4).
With this points calculating the area of the triangle.

A r e a (t r i a n g l e) = 12 × b a s e × h e i g h t A r e a (t r i a n g l e) = 12 × 12 × 4 A r e a (t r i a n g l e) = 24 s q u n i t s

Therefore, the area of the triangle formed is 24 sq units.

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