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

Perimeter of rectangle = ⇒
`18(1)/(6)` feet

Explanation:

Given:

Length of a rectangular sand box =
`5(1)/(3)\ feet`

Width of the box =
`3(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(1)/(3)+3(3)/(4))\ feet`

Simplifying by adding fractions:

⇒
`2(5+3+(1)/(3)+(3)/(4))\ feet` (Adding whole numbers and fractions separately)

⇒
`2(8+(1)/(3)+(3)/(4))` feet

Whole number 8 can be written as
`(8)/(1)`

⇒
`2((8)/(1)+(1)/(3)+(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((8* 12)/(1* 12)+(1* 4)/(3* 4)+(3* 3)/(4* 3))` feet

⇒
`2((96)/(12)+(4)/(12)+(9)/(12))` feet

Then we simply add numerators.

⇒
`2((96+4+9)/(12))` feet

⇒
`2((109)/(12))` feet

⇒
`2* (109)/(12)` feet

⇒
`(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(2)/(12)` feet

Simplifying fractions to simplest form.

⇒
`18(1)/(6)` feet

Perimeter =⇒
`18(1)/(6)` feet (Answer)