what is the easiest and fastest way to solve this?

Nine playing cards from the same deck are placed as shown in the figure below to form a large rectangle of area 180 sq. in. How many inches are there in the perimeter of this large rectangle?

Question

what is the easiest and fastest way to solve this?

Nine playing cards from the same deck are placed as shown in the figure below to form a large rectangle of area 180 sq. in. How many inches are there in the perimeter of this large rectangle?

anonymous · Answer

|dw:1343519419666:dw| they are all the same size I just can't draw

anonymous · Answer

This can be anything....

anonymous · Answer

do we know the measurements of the cards or a better picture?

anonymous · Answer

|dw:1343519858074:dw|
does that make you happy?

anonymous · Answer

w*l=180
2*w+2*l=?

This is a system of equations with an infinite number of solutions because we don't have enough information

anonymous · Answer

Iit HAS an answer the answer is 58 but I don't know how to get there

unklerhaukus · Answer

$$P=6\ell+7w$$

anonymous · Answer

The short sides are 4s and the longer ones are 5s

unklerhaukus · Answer

$$A=5w\times(w+l)$$

anonymous · Answer

From the illustration we can see that 5 breadths are equal to 4 lengths, which is equal to the length of the whole rectangle.

5b = 4l = L

We also know the area of the large rectangle. From this we can create a system of equations, which we can use to solve. Notice also that the height of the rectangle is equal to a breadth and a length.

h = b + l

Now for the system of equations, which expresses the area (given by A = h*L):

(b+l)*5b=180    (1)
(b+l)*4l=180     (2)

If we solve this system of equations we will get a value for the breadth and width, which we can use to find the perimeter.

anonymous · Answer

okay so 5b^2+5Bl=180
and       4lb+4l^2=180
then use the process of elimination?