The base of the triangle is 4 + 4 = 8 so the total perimeter is 5 + 5 + 8 = 18.

This Isosceles triangle has two sides with a length of \(\displaystyle \small \frac{3}{9}\) foot and one side length that is half of the length of the two equivalent sides. 

To find the missing side, double the value of side \(\displaystyle \small a\)'s denominator:

\(\displaystyle \small \frac{3}{9}=\frac{1}{3}\). Thus, half of \(\displaystyle \small \frac{1}{3}=\frac{1}{6}\).

Therefore, this triangle has two sides with lengths of \(\displaystyle \small \frac{1}{3}\) and one side length of \(\displaystyle \small \frac{1}{6}\). 

To find the perimeter, apply the formula: 

\(\displaystyle \small p=2a+b\)

\(\displaystyle \small p=\frac{1}{3}+\frac{1}{3}+\frac{1}{6}\)

\(\displaystyle \small p=\frac{2}{6}+\frac{2}{6}+\frac{1}{6}=\frac{5}{6}=\frac{10}{12}\) foot \(\displaystyle \small = 10\) inches

To solve this problem apply the formula: \(\displaystyle \small p=2a+b\).

However, first calculate the length of the missing side by: \(\displaystyle \small 13\div2=6.5\).

Thus, the solution is:

\(\displaystyle \small p=13+13+6.5=32.5\)

To solve this problem apply the formula: \(\displaystyle \small p=2a+b\).

However, first calculate the length of the missing side by:

\(\displaystyle \small p=2(a)+12\)

\(\displaystyle \small a=12\times5=60\)

\(\displaystyle \small p=2(60)+12\)

\(\displaystyle \small p=120+12=132\)

By definition, an Isosceles triangle must have two equivalent side lengths. Since we are told that \(\displaystyle b=\frac{3}{4}\) ft and that the sides with length \(\displaystyle a\) are half the length of side \(\displaystyle b\), find the length of \(\displaystyle a\) by: \(\displaystyle \frac{3}{4}=\frac{6}{8}\) and half of \(\displaystyle \frac{6}{8}=\frac{3}{8}\). Thus, both of sides with length \(\displaystyle a\) must equal \(\displaystyle \frac{3}{8}\) ft. 

Now, apply the formula: \(\displaystyle p=2a+b\).

\(\displaystyle p=\frac{3}{8}+\frac{3}{8}+\frac{6}{8}=\frac{12}{8}\)

Then, simplify the fraction/convert to mixed number fraction:


\(\displaystyle \frac{12}{8}=\frac{3}{2}=1\frac{1}{2}\)
 

In order to solve this problem, first find the length of the missing sides. Then apply the formula: \(\displaystyle \small p=2a+b\)

Each of the missing sides equal: 

\(\displaystyle \small a=\frac{7}{3}\times4=\frac{28}{3}\) 

Then apply the perimeter formula:
\(\displaystyle \small p=\frac{28}{3}+\frac{28}{3}+\frac{7}{3}=\frac{63}{3}=21\)

In order to solve this problem, first find the length of the missing sides. Then apply the formula: \(\displaystyle \small p=2a+b\)

The missing side equals:

\(\displaystyle b=\sqrt[3]{a}=\sqrt[3]{8}=2\)

Then plug each side length into the perimeter formula:

\(\displaystyle p=2(8)+2=16+2=18\)

 

In order to solve this problem, first find the length of the missing sides. Then apply the formula: \(\displaystyle \small p=2a+b\)

The missing side equals:

\(\displaystyle \small a=\sqrt{144}=12\)

\(\displaystyle \small b=12\times \frac{1}{2}=\frac{12}{2}=6\)

Then, apply the perimeter formula by plugging in the side values: 

\(\displaystyle \small p=2(12)+6=24+6=30\)

To solve this problem apply the formula: \(\displaystyle \small p=2a+b\).

However, first calculate the length of the missing side by:

\(\displaystyle \small \frac{3}{12}+\frac{3}{12}+(\frac{3}{12}\times\frac{1}{3})\) , Note that \(\displaystyle \small \frac{3}{36}=\frac{1}{12}\)


\(\displaystyle \small \small \frac{6}{12}+\frac{3}{36}=\frac{6}{12}+\frac{1}{12}=\frac{7}{12}\). 

Since, it takes \(\displaystyle \small 12\) inches to make one foot, the perimeter is equal to \(\displaystyle \small 7\) inches. 

To find the perimeter of this triangle, apply the formula: 

\(\displaystyle \small p=2a+b\)

\(\displaystyle \small p=2(8)+(8\times \frac{1}{4})\)

\(\displaystyle \small p=16+\frac{8}{4}\)

\(\displaystyle \small p=16+2=18\)

Note: Since this is an acute Isosceles triangle, the length of the base must be smaller than the length of both of the equivalent sides.