Question

The width of a picture frame is 16 3/5 centimeters. It’s length is 4 4/5 centimeters longer than the width . Find the length and the perimeter of the picture frame. Write the answer in simplest form.

Answer 1

`\begin{gathered} \text{Length = 21}(2)/(5)\text{ centimeters} \\ \\ \text{Perimeter = 76 centimeters} \end{gathered}`

Step-by-step explanation:

Since the length is 4⅘ longer than the width, the length will be:

Length = 4⅘ + 16⅗

`\begin{gathered} W\text{ = 16}(3)/(5)\text{ centimeters} \\ Length\text{ = 4}(4)/(5)\text{ }_{}+\text{ 16 }(3)/(5) \end{gathered}`

Let's solve for length:

`\begin{gathered} Length\text{ = 4}(4)/(5)\text{ }_{}+\text{ 16 }(3)/(5)\text{ = }(24)/(5)\text{ + }(83)/(5)\text{ = }(107)/(5)\text{ = 21}(2)/(5)\text{ centimeters} \\ \\ \text{Length = 21}(2)/(5)\text{ centimeters} \end{gathered}`

From the given dimensions, it shows the picture frame is a rectangle.

To find the perimeter, use the perimeter of a rectangle formula:

Perimeter of a rectangle = 2(Length + Width)

`\begin{gathered} \text{Perimeter = 2(}(107)/(5)+(83)/(5)) \\ \\ \text{ = 2(}(190)/(5)) \\ \\ \text{ = }2(38) \\ \\ \text{ = 76 centimeters} \end{gathered}`