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

ANSWER:

$\begin{gathered} \text{Length = 21}\frac{2}{5}\text{ centimeters} \\ \\ \text{Perimeter = 76 centimeters} \end{gathered}$

EXPLANATION:

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

Length = 4⅘ + 16⅗

$\begin{gathered} W\text{ = 16}\frac{3}{5}\text{ centimeters} \\ Length\text{ = 4}\frac{4}{5}\text{ }_{}+\text{ 16 }\frac{3}{5} \end{gathered}$

Let's solve for length:

$\begin{gathered} Length\text{ = 4}\frac{4}{5}\text{ }_{}+\text{ 16 }\frac{3}{5}\text{ = }\frac{24}{5}\text{ + }\frac{83}{5}\text{ = }\frac{107}{5}\text{ = 21}\frac{2}{5}\text{ centimeters} \\ \\ \text{Length = 21}\frac{2}{5}\text{ centimeters} \end{gathered}$

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)

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