Question

A rectangle sand box has a length of 5 and 1/3 feet and a width of 3 and 3/4 feet. What is the perimeter?

Answer 1

Answer:

Perimeter of rectangle = ⇒ $18\frac{1}{6}$ feet

Step-by-step explanation:

Given:

Length of a rectangular sand box = $5\frac{1}{3}\ feet$

Width of the box = $3\frac{3}{4}\ feet$

Perimeter of a rectangle = $2(l+w)$

where $l$ represents length of rectangle and $w$ represents width of the rectangle.

Substituting values given for length and width.

Perimeter of sand box = $2(5\frac{1}{3}+3\frac{3}{4})\ feet$

Simplifying by adding fractions:

⇒  $2(5+3+\frac{1}{3}+\frac{3}{4})\ feet$ (Adding whole numbers and fractions separately)

⇒  $2(8+\frac{1}{3}+\frac{3}{4})$ feet

Whole number 8 can be written as $\frac{8}{1}$

⇒  $2(\frac{8}{1}+\frac{1}{3}+\frac{3}{4})$ feet

To add fractions we take LCD for the denominators 3,4,1.

LCD for 3 and 4 = 12 as its the least common multiple of 3,4,1.

Making denominators =12 by multiplying numerator an denominator with the corresponding numbers

⇒  $2(\frac{8\times 12}{1\times 12}+\frac{1\times 4}{3\times 4}+\frac{3\times 3}{4\times 3})$ feet

⇒  $2(\frac{96}{12}+\frac{4}{12}+\frac{9}{12})$ feet

Then we simply add numerators.

⇒  $2(\frac{96+4+9}{12})$ feet

⇒  $2(\frac{109}{12})$ feet

⇒  $2\times \frac{109}{12}$ feet

⇒  $\frac{218}{12}$ feet

Writing fraction as a mixed number by dividing 218 by 12 and writing quotient as whole number and remainder as numerator with divisor as denominator.

⇒ $18\frac{2}{12}$ feet

Simplifying fractions to simplest form.

⇒ $18\frac{1}{6}$ feet

Perimeter =⇒ $18\frac{1}{6}$ feet  (Answer)