Question

Please help quick
A rectangular garden has length twice as great as is width a second rectangular has the same length as the first garden and width that is 4 meters greater than width of the first garden the second garden has area of 120 square meters what is the length of the two gardens?

Answer 1

First garden information:  let w = the width of the garden, then 2w = the length of the garden.

Second garden information:  
(w + 4) = the width  and 2w = the length;  the area is equal to 120

Now taking the information of the second garden we can set up the following equation:   2w(w + 4) = 120 or the following quadratic 2w² + 8w - 120 = 0
Now solving this quadratic by factoring we see that the solutions are:
w = -10 and w = 6 ... of these two solutions only w = 6 makes sense.

With w = 6,  the length of the two gardens would be 12

Answer 2

Answer:

6 meters is the length of the two gardens

Step-by-step explanation:

Bigger rectangle :

Width of the bigger rectangle  = W

Length of the bigger rectangle : L = 2W

Smaller rectangle :

Width of the smaller rectangle : w = W+4

Length of the smaller rectangle :l =  L = 2W

Area of the smaller rectangle, a = $120 m^2$

$a=l\times w$

$120 =(2W)\times (W+4)$

$120 = 2w^2+8W$

$2W^2+8W-120=0$

$W^2+4W-60=0$

$W^2+10W-6W-60=0$

$W(W+10)-6(W+10)=0$

$(W+10)(W-6)=0$

W = -10 (reject, negative)

W = 6

Length of the bigger rectangle : L = 2W = 2 × 6 m = 12 m

Length of the smaller rectangle : L = 2W = 2 × 6 m = 12 m

12 meters is the length of the two gardens