Draw in the height to create a right triangle.

Now, using the relationship between the lengths of sides in a $\displaystyle 30-60-90$ triangle, where the long leg is the short leg times $\displaystyle \sqrt 3$ and the hypotenuse is two times the short leg, we can find out that the height of the triangle is $\displaystyle \frac{3}{2}$ and the hypotenuse is $\displaystyle 3$.

The dashes on two sides of the triangle indicate that these two sides are congruent. The three side lengths of the triangle are $\displaystyle 3, 3, \text{and }3\sqrt3$.

Now, add up these side lengths to find the perimeter.

$\displaystyle \text{Perimeter}=3+3+3\sqrt3=11.2$

Draw in the height to create a right triangle.

Now, using the relationship between the lengths of sides in a $\displaystyle 30-60-90$ triangle, where the long leg is the short leg times $\displaystyle \sqrt3$ and the hypotenuse is twice the length of the short leg, we can find out that the height of the triangle is $\displaystyle 4$ and the hypotenuse is $\displaystyle 8$.

The dashes on two sides of the triangle indicate that these two sides are congruent. The three side lengths of the triangle are $\displaystyle 8, 8, \text{ and }8\sqrt3$.

Now, add up these side lengths to find the perimeter.

$\displaystyle \text{Perimeter}=8+8+8\sqrt3=29.9$

Draw in the height to create a right triangle.

Now, using the relationship between the lengths of sides in a $\displaystyle 30-60-90$ triangle, we can find out that the height of the triangle is $\displaystyle x$ and the hypotenuse is $\displaystyle 2x$.

The ratio of the sides in a $\displaystyle 30-60-90$ triangle are: $\displaystyle x:x\sqrt3:2x$.

The dashes on two sides of the triangle indicate that these two sides are congruent. The three side lengths of the triangle are $\displaystyle 2x, 2x, \text{ and }2x\sqrt3$.

Now, add up these side lengths to find the perimeter.

$\displaystyle \text{Perimeter}=2x+2x+2x\sqrt3=4x+2x\sqrt3$

Draw in the height to create a right triangle.

Now, using the relationship between the lengths of sides in a $\displaystyle 30-60-90$ triangle, we can find out that the height of the triangle is $\displaystyle 21x$ and the hypotenuse is $\displaystyle 42x$.

The ratio of the sides in a $\displaystyle 30-60-90$ triangle are: $\displaystyle x:x\sqrt3:2x$.

The dashes on two sides of the triangle indicate that these two sides are congruent. The three side lengths of the triangle are $\displaystyle 42x, 42x, \text{ and }42x\sqrt3$.

Now, add up these side lengths to find the perimeter.

$\displaystyle \text{Perimeter}=42x+42x+42x\sqrt3=84x+42x\sqrt3$

Draw in the height to create a right triangle.

Now, using the relationship between the lengths of sides in a $\displaystyle 30-60-90$ triangle, we can find out that the height of the triangle is $\displaystyle 8$ and the hypotenuse is $\displaystyle 16$.

The ratio of the sides in a $\displaystyle 30-60-90$ triangle are: $\displaystyle x:x\sqrt3:2x$.

The dashes on two sides of the triangle indicate that these two sides are congruent. The three side lengths of the triangle are $\displaystyle 16, 16, \text{ and }16\sqrt3$.

Now, add up these side lengths to find the perimeter.

$\displaystyle \text{Perimeter}=16+16+16\sqrt3=59.7$

Draw in the height to create a right triangle.

Now, using the relationship between the lengths of sides in a $\displaystyle 30-60-90$ triangle, we can find out that the height of the triangle is $\displaystyle 18x$ and the hypotenuse is $\displaystyle 36x$.

The ratio of the sides in a $\displaystyle 30-60-90$ triangle are: $\displaystyle x:x\sqrt3:2x$.

The dashes on two sides of the triangle indicate that these two sides are congruent. The three side lengths of the triangle are $\displaystyle 36x, 36x, \text{ and }36x\sqrt3$.

Now, add up these side lengths to find the perimeter.

$\displaystyle \text{Perimeter}=36x+36x+36x\sqrt3=72x+36x\sqrt3$

In order to find the perimeter of the triangle, we will first need to find the length of each side of the triangle by using the distance formula.

Recall the distance formula for a line:

$\displaystyle \text{distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The first side of the triangle is the line segment made with $\displaystyle (1, 5)\text{ and }(2, 12)$ as its endpoints.

$\displaystyle \text{side 1}=\sqrt{(2-1)^2+(12-5)^2}=\sqrt{50}=5\sqrt2$

The second side of the triangle is the line segment that has $\displaystyle (2, 12)\text{ and }(-3, 4)$ as its endpoints.

$\displaystyle \text{side 2}=\sqrt{(2-(-3))^2+(12-4)^2}=\sqrt{89}$

The third side of the triangle is the line segment that has $\displaystyle (-3, 4)\text{ and }(1, 5)$ as its endpoints.

$\displaystyle \text{side 3}=\sqrt{(1-(-3))^2+(5-4)^2}=\sqrt{17}$

Now, add up these three sides with a calculator to find the perimeter of the triangle.

$\displaystyle \text{Perimeter}=5\sqrt{2} +\sqrt{89}+\sqrt{17}=20.63$

Make sure to round to $\displaystyle 2$ places after the decimal.

In order to find the perimeter of the triangle, we will first need to find the length of each side of the triangle by using the distance formula.

Recall the distance formula for a line:

$\displaystyle \text{distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The first side of the triangle is the line segment made with $\displaystyle (5, 6)\text{ and }(7, 2)$ as its endpoints.

$\displaystyle \text{side 1}=\sqrt{(7-5)^2+(2-6)^2}=\sqrt{20}=2\sqrt5$

The second side of the triangle is the line segment that has $\displaystyle (7, 2)\text{ and }(9, 11)$ as its endpoints.

$\displaystyle \text{side 2}=\sqrt{(9-7)^2+(11-2)^2}=\sqrt{85}$

The third side of the triangle is the line segment that has $\displaystyle (5, 6)\text{ and }(9, 11)$ as its endpoints.

$\displaystyle \text{side 3}=\sqrt{(9-5)^2+(11-6)^2}=\sqrt{41}$

Now, add up these three sides with a calculator to find the perimeter of the triangle.

$\displaystyle \text{Perimeter}=2\sqrt{5} +\sqrt{85}+\sqrt{41}=20.09$

Make sure to round to $\displaystyle 2$ places after the decimal.

In order to find the perimeter of the triangle, we will first need to find the length of each side of the triangle by using the distance formula.

Recall the distance formula for a line:

$\displaystyle \text{distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The first side of the triangle is the line segment made with $\displaystyle (-5, 1)\text{ and }(6, -2)$ as its endpoints.

$\displaystyle \text{side 1}=\sqrt{(6-(-5))^2+(-2-1)^2}=\sqrt{130}$

The second side of the triangle is the line segment that has $\displaystyle (6, -2)\text{ and }(7, 0)$ as its endpoints.

$\displaystyle \text{side 2}=\sqrt{(7-6)^2+(0-(-2))^2}=\sqrt{5}$

The third side of the triangle is the line segment that has $\displaystyle (-5, 1)\text{ and }(7, 0)$ as its endpoints.

$\displaystyle \text{side 3}=\sqrt{(7-(-5))^2+(0-1)^2}=\sqrt{145}$

Now, add up these three sides with a calculator to find the perimeter of the triangle.

$\displaystyle \text{Perimeter}=\sqrt{130} +\sqrt{5}+\sqrt{145}=25.68$

Make sure to round to $\displaystyle 2$ places after the decimal.

In order to find the perimeter of the triangle, we will first need to find the length of each side of the triangle by using the distance formula.

Recall the distance formula for a line:

$\displaystyle \text{distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The first side of the triangle is the line segment made with $\displaystyle (9, 8)\text{ and }(12, 0)$ as its endpoints.

$\displaystyle \text{side 1}=\sqrt{(12-9)^2+(0-8)^2}=\sqrt{73}$

The second side of the triangle is the line segment that has $\displaystyle (12, 0)\text{ and }(-1, -2)$ as its endpoints.

$\displaystyle \text{side 2}=\sqrt{(-1-12)^2+(-2-0)^2}=\sqrt{173}$

The third side of the triangle is the line segment that has $\displaystyle (9, 8)\text{ and }(-1, -2)$ as its endpoints.

$\displaystyle \text{side 3}=\sqrt{(-1-9))^2+(-2-8)^2}=\sqrt{200}=10\sqrt2$

Now, add up these three sides with a calculator to find the perimeter of the triangle.

$\displaystyle \text{Perimeter}=\sqrt{73} +\sqrt{173}+10\sqrt{2}=35.84$

Make sure to round to $\displaystyle 2$ places after the decimal.