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Question

The area of the triangle formed by the line x + 3y = 12 and the coordinate axes is
(a) 12 sq units
(b) 18 sq units
(c) 24 sq units
(d) 30 sq units

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Solution

(c) 24 sq units
Given: x + 3y = 12 or, y = 12 - x3

When x = 0, then y = 123 = 4

When x = 3, then y = 93 = 3

When x = 6, then y =63 = 2

When x = 9, then y = 33 = 1

When x = 12, then y = 03 = 0

Thus, we get the following table:
x 0 3 6 9 12
y 4 3 2 1 0

Plot these points on the graph paper. Join them to get a right-angled triangle AOE, such that
AO = 4 unit and OE = 12 unit.


Therefore,
area ofAOE =12 (base × height) = 12(OE × AO) = 12×12×4 = 24 sq units


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