Question

3. Which triangle is possible?A. 4 in, 4 in, and 8 in.B. 4 yd, 5 yd, and 10 yd.C. 3 ft, 4 ft, and 5 ft.D. 3 ft, 3 ft, and 7 ft.

Answer 1

`C.\text{ }3ft,\text{ }4ft,\text{ }and\text{ }5ft.`

Step-by-step explanation

We want to find the triangle that is possible.

To do this, we have to apply the triangle inequality theorem that states that:

This implies that if we pick any two side lengths of a triangle, the sum of those lengths must be greater than the third side, and this applies for any two sides.

Hence, the only triangle among the options that obeys this theorem is:

`\begin{gathered} 3+4=7>5 \\ 3+5=8>4 \\ 4+5=9>3 \end{gathered}`

The correct answer is:

`C.\text{ }3ft,\text{ }4ft,\text{ }and\text{ }5ft.`