AlgebraHardArea of the triangle a line makes with the axes
Algebra practice question
In the xy-plane, the graph of 3x + 4y = 24 and the two coordinate axes form a triangle. What is the area of the triangle?
Answer: 24
The x-intercept is at 3x = 24, x = 8; the y-intercept is at 4y = 24, y = 6. The right triangle has legs 8 and 6, so its area is (1/2)(8)(6) = 24.
Common wrong answers
- If you answered 12
- 12 comes from halving the area a second time.
- If you answered 14
- 14 is 8 + 6, the sum of the intercepts.
- If you answered 48
- 48 is 8 × 6, without the half.
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