Mathematics

Problem

In solving for the unknown side

x

of a triangle with other sides 4 cm and 5 cm and area 6

\text{cm}^2

, a quadratic equation gives the roots

x = 3

cm and

x = 12

cm. Which choice correctly identifies the valid value of

x

? a)

\text{Both }3\text{ cm and }12\text{ cm, since both roots are positive}

3\text{ cm, because the three lengths satisfy the triangle inequality}

12\text{ cm, because the larger root corresponds to the given area}

\text{Neither value, because the triangle inequality is not met}