Question

If the area of triangle formed by the lines x = 0, y = 0 and 4x + 3y = a is 5 square units, then a² =

• A. 140
• B. 120
• C. 300
• D. 400

Answer 1

Answer: (B)

120

Answer 2

The lines $x=0$, $y=0$, and $4x+3y=a$ form a triangle with vertices at $(0,0)$, $(a/4, 0)$, and $(0, a/3)$. This is a right-angled triangle with base $|a/4|$ and height $|a/3|$. The area is $\frac{1}{2} \times |\frac{a}{4}| \times |\frac{a}{3}| = \frac{a^2}{24}$. Given the area is 5, we have $\frac{a^2}{24} = 5$. Solving for $a^2$ gives $a^2 = 5 \times 24 = 120$.