Multiplying Binomials

You are planning a rectangular garden. Its length is twice its width. You want a walkway 2 ft wide around the garden.
a. Write an expression for the area of the garden and walk.
b. Write an expression for the area of the walk only.
c. You have enough gravel to cover 76 square feet and want to use it all on the walk. How big should you make the garden?

I checked Hotmath, but it didn't explain it very well. In the back of my textbook, it says the answers are:

a. 2x^2+12x+16
b. 12x+16
c. 10 ft by 5 ft

I do not know how they get the answers. I think I drew my picture wrong of the whole situation. If someone could help it would be GREATLY appreciated!

Well, start with L=2w

area walkway= 2 L + 2W + 4*2*2 the last term is the corners.
Now add the area of the garden, and either change the terms to all W, or or all L. THe answer will depend on which one your choose. Either x is L, or w.

set 76 equal to the area of the sidewalk above. Solve for either L or W. Once that is done, solve for the other.
LW is the area of the garden.

I get all the other stuff, but I still don't understand how you get the "16" for the formula for the walkway. I only see variables in the problem, but I don't know how to get the constant in there. Thanks so much for helping!

if the walks around the area have INSIDE lenths L and widths W, then are 2 feet wide, you have to add the four corners to the area of the walkway (2ftx2ft each). Area walkway= 2L + 2W + 4*2*2

OH! I get it now! Thank you so much for your help! I <3 this website!

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  1. WHATS (3N=2)(N+3)

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