A design calls for a rectangular garden with an area of 180 square feet. If the length is to be 3 feet more than the width, set up an equation and solve that equation to find the dimensions of the garden.

I drew a sketch and labeled the width "w" and the length "w+3"

my equation was:

w(w+3)=180

simplified and split the middle term:

w^2+15w-12w-180=0

should I group again?
thanks, meloney

Hey, Mel!

Well, w^2 + 15w - 12w - 180 = 0.

Turns into:

w^2 + 3w - 180 = 0.

Then, you can either split the middle form (take 2) or you can do the other thing (don't know how to explain it... but you know what I mean by take 1, right?)

If you need any more help, tell me. :-)

my equation is splitting the middle term emmalene. sigh.

w^2 + 15w - 12w - 180 = 0

pull out the GCF of each pair.
w(w + 15) - 12(w + 15) = 0

then pull out the common factor (w + 15) from eatch term.
(w + 15)(w - 12) = 0

see if you can take it from there.

thanks so much!!!

Yes, you should group the terms again to simplify the equation further. By combining like terms, you can simplify the equation from:

w^2 + 15w - 12w - 180 = 0

To:

w^2 + 3w - 180 = 0

Now, you can solve this quadratic equation to find the dimensions of the garden. To do this, you can either factor the equation or use the quadratic formula.

Let's start by factoring the equation:

w^2 + 3w - 180 = 0

(w + 15)(w - 12) = 0

Now, set each factor equal to zero:

w + 15 = 0 or w - 12 = 0

Solving each equation will give you:

w = -15 or w = 12

Since the width cannot be a negative value, we discard w = -15. Therefore, the width of the garden is 12 feet.

Using the equation provided earlier, you can find the length by substituting the width:

w + 3 = 12 + 3 = 15

So, the length of the garden is 15 feet.

Therefore, the dimensions of the rectangular garden are 12 feet by 15 feet.