Question

A rectangle has side lengths of 1 3/4 feet and 2 1/3 feet. Find the perimeter of the rectangle. Write your answer as a mixed number in simplest form.

Answer 1

8 feet

Explanation:

Rectangles have congruent opposite side lengths. This means that if one of its longer sides were 2 1/3 feet and one of its shorter sides were 1 3/4 feet then the other longer side would also be 2 1/3 feet and the other shorter side would be 1 3/4 feet.

Therefore to find the perimeter, you would take the given side lengths and multiply them each by 2 to account for both of the congruent sides.

• 2(2 1/3) + 2(1 3/4) = perimeter of rectangle

To multiply these fractions they would have to be converted into improper fractions. Multiply the whole number by the denominator and add the numerator---keeping the denominator the same in the converted form.

• 2 1/3 ⇒ 7/3
• 1 3/4 ⇒ 7/4

Now you can multiply these fractions by 2. Multiply the numerators by 2 and keep the denominator the same.

• 2(7/3) + 2(7/4)
• 14/3 + 14/4

To add them they should have common denominators so multiply 14/3 by 4/4 and 14/4 by 3/3.

• 14/3 (4/4) = 56/12
• 14/4 (3/3) = 42/12

Add 54/12 and 42/12 together by combining the numerators and keeping the denominators the same.

• 54/12 + 42/12 = 96/12

You can simplify this improper fraction even more by dividing 96 by 12 since 12 is a factor of 96.

• 96/12 = 8

The perimeter of the rectangle is 8 feet.

Answer 2

The perimeter of given rectangle is
`8(1)/(6)\text{ feet}`.

Explanation:

We are given the following information in the question:

Width of rectangle =

`1\displaystyle(3)/(4)\text{ feet}`

Length of rectangle =

`2\displaystyle(1)/(3)\text{ feet}`

Formula:

Perimeter of rectangle =

`2* (\text{Length + Width})`

Putting the values:

`2* (1\displaystyle(3)/(4) + 2(1)/(3))\\\\=2* ((7)/(4) + (7)/(3))\\\\=2* ((21+28)/(12))\\\\=2* (49)/(12)\\\\=(49)/(6)\\\\=8(1)/(6)`

Hence, the perimeter of given rectangle is
`8(1)/(6)\text{ feet}`.