SOLUTION: a rectangular garden has a perimeter of 44m. A walkway 2m wide surrounds the garden. The combined area of the garden and walkway is 224m2. What are the dimensions.

Question 188725This question is from textbook
: a rectangular garden has a perimeter of 44m. A walkway 2m wide surrounds the garden. The combined area of the garden and walkway is 224m2. What are the dimensions. This question is from textbook

Answer by jojo14344(1513) (Show Source): You can put this solution on YOUR website!

Let's picture out the garden wit the walkway.

We know for Rectangle, ---> , Eqn 1

, Eqn 2

Also we know, , Eqn 3

Now for the Combined Area (Garden + Walkway), we need to add "4 meters" for each Length and Width as shown.
New Length= L+2m+2m= L+4m; New Width= W+2m+2m = W+4m

Then going back Eqn 3, for the combined Area:
, substitute Eqn 2:

Expand right terms (multiply):
First terms:
Outer terms:
Inner terms:
Last terms:

Adding all results in red mark:

, divide by "-1" becomes---> , working eqn
*Remember
Solving discriminant:

Then, by quadratic:

Width of the Garden can either be W[1]=12m or W[2]=10m.

For Length, go back Eqn 2:

Or

Length can either be L[1]=10m or L[2]=12m

Let's check with the combined Area:

Thank you,
Jojo

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