Convert mixed fractions to decimals or improper fractions

Convert the width $w = 2 \frac{3}{4}$ to a decimal for easier calculation: $w = 2.75$ cm.

$w = 2 + \frac{3}{4} = 2.75$

Use the perimeter formula

The perimeter of a rectangle is defined as $P = 2 \times (l + w)$. Given $P = 13$, we have $13 = 2 \times (l + 2.75)$.

$13 = 2(l + 2.75)$

Solve for length l

Divide by 2: $6.5 = l + 2.75$. Then isolate $l$: $l = 6.5 - 2.75 = 3.75$.

$l = 3.75$

Convert result back to mixed fraction

Convert $3.75$ back to a mixed fraction: $3.75 = 3 \frac{75}{100} = 3 \frac{3}{4}$.

$l = 3 \frac{3}{4} \text{ cm}$