The dashes on the two sides of the triangle indicate that those two sides are congruent. Thus, the length of the missing side is $\displaystyle 2x-5$ also.

Now, use the information given about the perimeter to set up an equation to solve for $\displaystyle x$. The sum of all the sides will give the perimeter.

$\displaystyle 2x-5+2x-5+x=40$

$\displaystyle 5x-10=40$

$\displaystyle 5x=50$

$\displaystyle x=10$

The dashes on the two sides of the triangle indicate that those two sides are congruent. Thus, the length of the missing side is $\displaystyle x+3$ also.

Now, use the information given about the perimeter to set up an equation to solve for $\displaystyle x$. The sum of all the sides will give the perimeter.

$\displaystyle x+3+x+3+x=24$

$\displaystyle 3x+6=24$

$\displaystyle 3x=18$

$\displaystyle x=6$

The dashes on the two sides of the triangle indicate that those two sides are congruent. Thus, the length of the missing side is $\displaystyle 2x-2$ also.

Now, use the information given about the perimeter to set up an equation to solve for $\displaystyle x$. The sum of all the sides will give the perimeter.

$\displaystyle 2x-2+2x-2+3x-6=39$

$\displaystyle 7x-10=39$

$\displaystyle 7x=49$

$\displaystyle x=7$

To solve this problem, first work backwards using the formula: 

$\displaystyle Area=\frac{b\cdot h}{2}$

Plugging in the given information and solving for height.

$\displaystyle 24=\frac{6h}{2}$

$\displaystyle 24\times2=6h$

$\displaystyle 48=6h$

$\displaystyle h=\frac{48}{6}=8$

Now that you've found the height of the triangle, use the Pythagorean Theorem to find the length of one of the equivalent sides of the triangle. 

(Note, when applying the formula divide the measurement of the base in half--so the triangle will have sides of $\displaystyle 3, 8$ and $\displaystyle c^2$. 

Thus, the solution is:
$\displaystyle 3^2+8^2=c^2$
$\displaystyle 9+64=c^2$
$\displaystyle 73=c^2$

$\displaystyle c=\sqrt{73}$

In this problem, the isosceles triangle will have two sides with the length of $\displaystyle \sqrt{73}$ and one side length of $\displaystyle 6$. Therefore, the perimeter is: $\displaystyle 2\sqrt{73}+6$

To solve this problem, first convert each of the fractions from feet to inches. 

$\displaystyle \frac{3}{4}=\frac{9}{12}=9$ inches


$\displaystyle \frac{1}{4}=\frac{3}{12}=3$ inches


$\displaystyle \frac{2}{6}=\frac{4}{12}=4$ inches

The perimeter of the triangle must equal $\displaystyle 9+3+4=16$ 

Since the two side lengths provided in the question are not the hypotenuse, first use the Pythagorean Theorem to find the length of the third side. 

$\displaystyle a^2+b^2=c^2$

$\displaystyle 12^2+15^2=c^2$

$\displaystyle 144+225=c^2$

$\displaystyle c^2=369$

$\displaystyle c=\sqrt{369}=\sqrt{9}\sqrt{41}=3\sqrt{41}$

The perimeter is equal to $\displaystyle a+b+c$.

$\displaystyle 12+15+3\sqrt{41}$

$\displaystyle 3\sqrt{41}+27$

Since the two side lengths provided in the question are not the hypotenuse, first use the Pythagorean Theorem to find the length of the third side. 

$\displaystyle a^2+b^2=c^2$


$\displaystyle 2.5^2+4.5^2=c^2$


$\displaystyle 6.25+20.25=c^2$

$\displaystyle c^2=26.5$

$\displaystyle c=\sqrt{26.5}$


Perimeter is equal to $\displaystyle a+b+c$.

$\displaystyle 2.5+4.5+\sqrt{26.5}=7+ \sqrt{26.5}$

To solve this solution, first work backwards using the formula: $\displaystyle Area=\frac{b\cdot h}{2}$

$\displaystyle 32=\frac{8h}{2}$

$\displaystyle 8h=64$

$\displaystyle h=8$

Now that you've found the height of the triangle, use the Pythagorean Theorem to find the length of one of the equivalent sides of the triangle. 

(Note, when applying the formula divide the measurement of the base in half--so the triangle will have sides of $\displaystyle 4,8$ and $\displaystyle c^2$. 

Thus, the solution is:
$\displaystyle 4^2+8^2=c^2$

$\displaystyle 16+64=c^2$

$\displaystyle c^2=80$

$\displaystyle c=\sqrt{80}=4\sqrt{5}$

In this problem, the isosceles triangle will have two sides with the length of $\displaystyle 4\sqrt{5}$ and one side length of $\displaystyle 8$. Therefore, the perimeter is: $\displaystyle 8+8\sqrt{5}$.

Use the Pythagorean Theorem to find the length of one of the equivalent sides of the triangle. 

(Note, when applying the formula divide the measurement of the base in half--so the triangle will have sides of $\displaystyle 7,20$ and $\displaystyle c^2$. 

Thus, the solution is:
$\displaystyle 7^2+20^2=c^2$

$\displaystyle 49+400=c^2$

$\displaystyle c^2=449$

$\displaystyle c=\sqrt{449}$

In this problem, the isosceles triangle will have two sides with the length of $\displaystyle \sqrt{449}$ and one side length of $\displaystyle 14$. Therefore, the perimeter is: $\displaystyle 14+2\sqrt{449}$.

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 length of the short leg times $\displaystyle \sqrt3$ and the hypotenuse is two times the length of the short side. We can find out that the height of the triangle is $\displaystyle 3$ since it is the short leg and the hypotenuse is $\displaystyle 6$.

The dashes on two sides of the triangle indicate that these two sides are congruent. The three side lengths of the triangle are $\displaystyle 6, 6, \text{ and }6\sqrt3$.

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

$\displaystyle \text{Perimeter}=6+6+6\sqrt3=22.4$