Question

find the perimeter of the triangle to the right in simplified radical form. the perimeter of the triangle is (type an exact answer, using radicals as needed.)

Explanation:

Step1: Simplify each radical

• Simplify $\sqrt{48}$:

$$\sqrt{48}=\sqrt{16\times3}=\sqrt{16}\times\sqrt{3}=4\sqrt{3}$$

• Simplify $\sqrt{75}$:

$$\sqrt{75}=\sqrt{25\times3}=\sqrt{25}\times\sqrt{3}=5\sqrt{3}$$

Step2: Calculate the perimeter

The perimeter $P$ of a triangle is the sum of its side - lengths. Here, the side - lengths are $\sqrt{48}$, $\sqrt{48}$, and $\sqrt{75}$.
$$P = \sqrt{48}+\sqrt{48}+\sqrt{75}$$
Substitute the simplified radicals:
$$P=4\sqrt{3}+4\sqrt{3}+5\sqrt{3}$$
Combine like terms:
$$P=(4 + 4+5)\sqrt{3}=13\sqrt{3}$$

Answer:

$13\sqrt{3}$ m