Question

What is the greatest possible area of a triangle with one side of length 7 and another side of length 10 ?

• A. 17
• B. 34
• C. 35
• D. 70
• E. 140

Answer 1

The correct option is C 35

If the side of length $10$ is the base and the side of length $7$ is free to rotate to the point, where the altitude is greatest that will achieve the maximum area and will happen when it is perpendicular to the base.

The triangle will then have altitude $7$ and base $10$ (and be a right triangle), and its area is

$\therefore \frac{1}{2}\times 7\times 10=\frac{70}{2}=35$.