The length of a rectangular garden is 5 less than two times the width. There is a 5 foot wide sidewalk on 2 sides that has an area of 225 sq ft. How do you find the dimensions of the garden?

nyle2k8431

nyle2k8431

Answered question

2022-11-11

The length of a rectangular garden is 5 less than two times the width. There is a 5 foot wide sidewalk on 2 sides that has an area of 225 sq ft. How do you find the dimensions of the garden?

Answer & Explanation

Jaydon Roth

Jaydon Roth

Beginner2022-11-12Added 13 answers

Let x be the length of a rectangle and y is the width.
The first equation that can be derived from a condition "The length of a rectangular garden is 5 less than two times the width" is
x=2y−5

The story with a sidewalk needs clarification.
First question: is sidewalk inside the garden or outside?
Let's assume its outside because it seems more natural (a sidewalk for people going around the garden enjoying the beautiful flowers growing inside).
Second question: is sidewalk on two opposite sides of the garden or on two adjacent?
We should assume, the sidewalk goes along two adjacent sides, along the length and the width of the garden. It cannot be along opposite two sides because sides are different and the problem would not be properly defined.

So, a sidewalk of 5 foot wide goes along two adjacent sides of a rectangle, turning at 90 0 around the corner. Its area consists of the part going along the length of a rectangle (area is 5*x), along its width (area is 5*y) and includes the 5x5 square at the corner (area is 5*5).
This is sufficient to derive the second equation:
5x+5y+5*5=225
or
x+y=40

Now we have to solve a system of two equations with two unknown:
x=2y−5
x+y=40

Substituting 2y−5 from the first equation into the second for x:
2y−5+y=40
or
3y=45
or
y=15
from which
x=2*15−5=25
So, the garden has dimensions 25x15.

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