Question

the perimeter of a plane figure is the total distance around the figure. find the perimeter of the figure. the perimeter is ft (type an integer, proper fraction, or mixed number.) question 62, 1.3.98 63 correct points: 0 of 1

Explanation:

Step1: Recall perimeter formula

Perimeter is sum of all side - lengths.

Step2: Identify side - lengths

The side - lengths are $1\frac{2}{3}$ feet, $3\frac{8}{13}$ feet, $1\frac{3}{4}$ feet, $ \frac{3}{8}$ feet.

Step3: Convert mixed numbers to improper fractions

$1\frac{2}{3}=\frac{1\times3 + 2}{3}=\frac{5}{3}$, $3\frac{8}{13}=\frac{3\times13+8}{13}=\frac{47}{13}$, $1\frac{3}{4}=\frac{1\times4 + 3}{4}=\frac{7}{4}$, $\frac{3}{8}$ remains as is.

Step4: Find a common denominator

The common denominator of 3, 13, 4, and 8 is 312.
$\frac{5}{3}=\frac{5\times104}{3\times104}=\frac{520}{312}$, $\frac{47}{13}=\frac{47\times24}{13\times24}=\frac{1128}{312}$, $\frac{7}{4}=\frac{7\times78}{4\times78}=\frac{546}{312}$, $\frac{3}{8}=\frac{3\times39}{8\times39}=\frac{117}{312}$.

Step5: Add the fractions

$\frac{520 + 1128+546 + 117}{312}=\frac{2311}{312}=7\frac{127}{312}$

Answer:

$7\frac{127}{312}$