Question

Rashau made a rectangular frame for her latest oil painting. The length is 28 centimeters more than triple the width. The perimeter of the frame is 136 centimeters. Find the length and the width of the frame

Answer 1

The length is about 28 more than three times the width. Denoted as (a) width, and as (b) the length. Then move on to lay the system of equations, as done below:

$\begin{cases}2a+2b=136\\b=3a+28\end{cases}$
$\begin{cases}2a+2b=136|:2\\b=3a+28\end{cases}$
$\begin{cases}a+b=68\\b=3a+28\end{cases}$
$\begin{cases}a+3a+28=68\\b=3a+28\end{cases}$
$\begin{cases}4a=40|:4\\b=3a+28\end{cases}$
$\begin{cases}a=10\\b=3*10+28\end{cases}$
$\begin{cases}a=10\\b=58\end{cases}$

The short side has a length of 10 cm, and 58 cm long.