# The perimeter of a garden is 250 meters. the length is 5 meters more than 3 times the width, find the dimensions of the garden?

Aug 6, 2015

Width: 30 m
Length: 95 m

#### Explanation:

First, start by writing the formula for the perimeter of a rectangle

$P = 2 \cdot \left(L + w\right)$, where

$L$ - the length of the rectangle;
$w$ - the width of the rectangle;

This will be your first equation. To get the second one, use the fact that the length of the perimeter is 5 m more than 3 times its width.

$L = 3 \cdot w + 5$

Plug this into the first equation and solve for $w$ to get

$2 \cdot \left(3 w + 5 + w\right) = 250$

$8 w + 10 = 250$

$8 w = 240 \implies w = \frac{240}{8} = \textcolor{g r e e n}{\text{30 m}}$

This means that the length of th garden is

$L = 3 \cdot \left(30\right) + 5 = \textcolor{g r e e n}{\text{95 m}}$

Give it a quick check to see if the solutions match

$2 \cdot \left(30 + 95\right) = 250$

$2 \cdot 125 = 250 \text{ } \textcolor{g r e e n}{\sqrt{}}$