I need help solving this step by step I don't know where to begin

Question

An architect designs a rectangular flower garden such that the width is exactly two thirds of the length. If 300 feet of fencing find the dimensions Of the garden.

Answer 1

Hi Tyler

 

Let's see what we have.

 

For the garden

L = length

W = width

W = (2/3)L

 

Fencing = 300'

 

To enclose a garden we need to find the perimeter of the garden.

 

P = perimeter

P = 2(L+W)

 

Since W = (2/3)L, then

P = 2[L+(2/3)L] =300

 

Let's rewrite this so it's clear

2L + 4/3 L = 300

10/3 L = 300

L = 90

Since W = 2/3L, then 

W = 60

 

And to double check

2(L+W) = 2(60+90) = 2(150) = 300

 

The dimensions of the garden are 90' by 60'