Question

The straight lines $7x+2y-10=0$ and $72x+2y-10=0$ forms an isosceles triangle with the line $y=2$. Area of this triangle is equal to

• A. $\frac{15}{7}sq.units$
• B. $\frac{10}{7}sq.units$
• C. $\frac{18}{7}sq.units$
• D. $\frac{10}{13}sq.units$

Answer 1

Answer: (C)

$\frac{18}{7}sq.units$

$7x+2y-10=0$

Plotting the lines on a graph gives us isosceles triangle with base as line y=2.

Vertices are $(0,5),(\frac{-6}{7},2),(\frac{6}{7},2)$

Area = $\frac{1}{2}\times base\times height$

Clearly height is 3 units and base is $2\times \frac{6}{7}$ units

Area = $\frac{1}{2}\times \frac{12}{7}\times 3$

= $\frac{18}{7}sq.units$