An architect designs a rectangular flower garden such that the width is exactly two-thirds of the length. if 340 feet of antique picket fencing are used to enclosed the garden find the dimensions of the garden

l=102 feet, w=68 feet

Step-by-step explanation:

Let w=width and l=length

P=2l + 2w

And we know that w=2/3l

So, using substitution...

340=2l + 2(2/3l)

340=2l + 4/3l

340=6/3l + 4/3l

340=10/3l (now multiply both sides by 3 to get rid of fraction)

1020=10l

So l=102

Now plug in to get w

2(102)+2w=340

204+2w=340

2w=136

w=68

Now check:

2(102)+2(68)=

204+136=

340 It works!

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