Maximizing Triangle Area with Sides

A triangle has sides of lengths a, b, and c, which are represented as follows:

• a = 5 cm
• b = 12 cm
• c is unknown but must form a valid triangle with a and b.

The area of the triangle is given by the formula:

$$A =\frac{1}{2} imes ext{base} imes ext{height}$$

In this case, if c is such that it forms an isosceles triangle with a and b, what is the possible length of c such that the area of the triangle is maximized? Choose the closest option for c given that the height from c to the base (when c is the base) should be perpendicular to the base.