Question

the perimeter of a rectangle is 30 meters and the length is 5 meters longer than the width. find the dimensions of the rectangle. let $x$ = the length and $y$ = the width.
the corresponding modeling system is $\

$$\begin{cases}2x + 2y = 30 \\\\ x - y = 5\\end{cases}$$

$. use the method of substitution to solve this system.
answer
length of the rectangle = $square$ m.
width of the rectangle = $square$ m

Explanation:

Step1: Isolate $x$ from second equation

$x = y + 5$

Step2: Substitute $x$ into first equation

$2(y + 5) + 2y = 30$

Step3: Simplify and solve for $y$

$2y + 10 + 2y = 30$
$4y = 20$
$y = 5$

Step4: Substitute $y$ back to find $x$

$x = 5 + 5 = 10$

Answer:

Length of the rectangle = 10 m
Width of the rectangle = 5 m